diff --git a/gpx-rs/engine/src/engine/action.rs b/gpx-rs/engine/src/engine/action.rs
index 833e7d3ef..6f6aeb310 100644
--- a/gpx-rs/engine/src/engine/action.rs
+++ b/gpx-rs/engine/src/engine/action.rs
@@ -3,13 +3,22 @@ use crate::{Command, FileId};
 /// Everything the frontend can ask the engine to do.
 ///
 /// Only [`Action::Edit`] changes the files (and records an undo step); the others act on the
-/// history or on the selection.
+/// history, on the selection or on the file order.
 #[derive(Debug)]
 pub enum Action<'a> {
     Edit(Command<'a>),
     Undo,
     Redo,
-    Select { file_ids: Vec<FileId> },
-    AddSelect { file_ids: Vec<FileId> },
+    Select {
+        file_ids: Vec<FileId>,
+    },
+    AddSelect {
+        file_ids: Vec<FileId>,
+    },
     SelectAll,
+    /// Moves the files to `index` among the other files, in the given order. Not undoable.
+    Reorder {
+        file_ids: Vec<FileId>,
+        index: usize,
+    },
 }
diff --git a/gpx-rs/engine/src/engine/engine.rs b/gpx-rs/engine/src/engine/engine.rs
index 105f2d9cc..8c0988499 100644
--- a/gpx-rs/engine/src/engine/engine.rs
+++ b/gpx-rs/engine/src/engine/engine.rs
@@ -45,6 +45,7 @@ impl Engine {
                 }
                 true
             }
+            Action::Reorder { file_ids, index } => self.order.move_files(&file_ids, index),
             Action::SelectAll => {
                 self.selection = Selection::File {
                     file_ids: self.order.0.iter().copied().collect(),
@@ -74,6 +75,17 @@ impl Engine {
     /// Brings everything derived from the files back in line with the current stack entry.
     fn refresh(&mut self) {
         let current = self.stack.current();
+        match current {
+            Some(files) => {
+                // files coming back after an undo/redo are added at the end of the order
+                self.order.sync(files);
+                self.selection.retain_existing(files);
+            }
+            None => {
+                self.order.0.clear();
+                self.selection = Selection::Empty;
+            }
+        }
         self.statistics_cache.update(current);
         self.statistics_buffer
             .update(&self.statistics_cache.get(current, &self.selection));
@@ -240,6 +252,34 @@ mod tests {
         assert!(engine.stack.current().is_none());
     }
 
+    #[test]
+    fn test_reorder_is_not_undoable_and_returning_files_go_last() {
+        let mut engine = Engine::default();
+        new(&mut engine, "a");
+        let a = engine.order.0[0];
+        new(&mut engine, "b");
+        let b = engine.order.0[1];
+        new(&mut engine, "c");
+        let c = engine.order.0[2];
+
+        assert!(engine.execute(Action::Reorder {
+            file_ids: vec![c],
+            index: 0
+        }));
+        assert_eq!(engine.order.0, vec![c, a, b]);
+        assert!(!engine.execute(Action::Reorder {
+            file_ids: vec![c],
+            index: 0
+        }));
+
+        // undoing the creation of c does not undo the reorder
+        assert!(engine.execute(Action::Undo));
+        assert_eq!(engine.order.0, vec![a, b]);
+        // c comes back at the end
+        assert!(engine.execute(Action::Redo));
+        assert_eq!(engine.order.0, vec![a, b, c]);
+    }
+
     #[test]
     fn test_undo_updates_statistics() {
         let mut engine = Engine::default();
diff --git a/gpx-rs/engine/src/engine/state/order.rs b/gpx-rs/engine/src/engine/state/order.rs
index 5c63c027e..fce59cf67 100644
--- a/gpx-rs/engine/src/engine/state/order.rs
+++ b/gpx-rs/engine/src/engine/state/order.rs
@@ -1,4 +1,97 @@
-use crate::FileId;
+use std::collections::HashSet;
 
-#[derive(Debug, Default)]
+use crate::{FileId, StackEntry as Files};
+
+#[derive(Debug, Default, Clone, PartialEq, Eq)]
 pub struct FileOrder(pub Vec<FileId>);
+
+impl FileOrder {
+    /// Moves the given files, as a block and in the given order, so that they start at `index`
+    /// among the other files (clamped to the end). Unknown ids are ignored. Returns whether the
+    /// order changed.
+    pub fn move_files(&mut self, file_ids: &[FileId], index: usize) -> bool {
+        let mut seen = HashSet::new();
+        let moved: Vec<FileId> = file_ids
+            .iter()
+            .copied()
+            .filter(|id| self.0.contains(id) && seen.insert(*id))
+            .collect();
+        let mut order: Vec<FileId> = self
+            .0
+            .iter()
+            .copied()
+            .filter(|id| !seen.contains(id))
+            .collect();
+        let index = index.min(order.len());
+        order.splice(index..index, moved);
+        let changed = order != self.0;
+        self.0 = order;
+        changed
+    }
+
+    /// Drops the files that do not exist anymore and appends the new ones at the end.
+    pub fn sync(&mut self, files: &Files) {
+        self.0.retain(|id| files.contains_key(id));
+        let known: HashSet<FileId> = self.0.iter().copied().collect();
+        self.0
+            .extend(files.keys().filter(|id| !known.contains(id)).copied());
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn ids() -> [FileId; 3] {
+        [FileId::default(), FileId::default(), FileId::default()]
+    }
+
+    #[test]
+    fn test_move_files_as_block_in_given_order() {
+        let [a, b, c] = ids();
+        let mut order = FileOrder(vec![a, b, c]);
+        assert!(order.move_files(&[c, a], 1));
+        // index counts among the files that are not moved
+        assert_eq!(order.0, vec![b, c, a]);
+    }
+
+    #[test]
+    fn test_move_files_start_and_clamped_end() {
+        let [a, b, c] = ids();
+        let mut order = FileOrder(vec![a, b, c]);
+        assert!(order.move_files(&[c], 0));
+        assert_eq!(order.0, vec![c, a, b]);
+        assert!(order.move_files(&[c], 100));
+        assert_eq!(order.0, vec![a, b, c]);
+    }
+
+    #[test]
+    fn test_move_files_ignores_unknown_and_duplicate_ids() {
+        let [a, b, c] = ids();
+        let mut order = FileOrder(vec![a, b, c]);
+        assert!(order.move_files(&[FileId::default(), b, b], 0));
+        assert_eq!(order.0, vec![b, a, c]);
+    }
+
+    #[test]
+    fn test_move_files_unchanged() {
+        let [a, b, c] = ids();
+        let mut order = FileOrder(vec![a, b, c]);
+        assert!(!order.move_files(&[], 0));
+        assert!(!order.move_files(&[a, b], 0));
+        assert!(!order.move_files(&[FileId::default()], 0));
+        assert_eq!(order.0, vec![a, b, c]);
+    }
+
+    #[test]
+    fn test_sync_drops_missing_and_appends_new_at_the_end() {
+        let [a, b, c] = ids();
+        let mut files = Files::default();
+        for id in [b, c] {
+            files.insert(id, Default::default());
+        }
+        let mut order = FileOrder(vec![a, b]);
+        order.sync(&files);
+        assert_eq!(order.0, vec![b, c]);
+    }
+}
diff --git a/gpx-rs/wasm/src/lib.rs b/gpx-rs/wasm/src/lib.rs
index 2c1911e10..637208f02 100644
--- a/gpx-rs/wasm/src/lib.rs
+++ b/gpx-rs/wasm/src/lib.rs
@@ -141,6 +141,13 @@ pub fn delete_all() -> bool {
     edit(Command::DeleteAll(engine::DeleteAll))
 }
 
+/// Moves the files to `index` among the other files, in the given order (not undoable).
+/// `file_ids_bytes`: concatenated 16-byte UUIDs.
+#[wasm_bindgen]
+pub fn reorder(file_ids_bytes: &[u8], index: usize) -> bool {
+    file_ids(file_ids_bytes).is_some_and(|file_ids| execute(Action::Reorder { file_ids, index }))
+}
+
 // Edit commands
 
 #[wasm_bindgen]