diff --git a/slotmachine/__init__.py b/slotmachine/__init__.py
index a2ef3a0..f82e8ce 100644
--- a/slotmachine/__init__.py
+++ b/slotmachine/__init__.py
@@ -29,6 +29,7 @@ class Talk:
     preferred_venues: set[VenueID] = field(default_factory=set)
     allowed_slots: set[Slot] = field(default_factory=set)
     preferred_slots: set[Slot] = field(default_factory=set)
+    must_schedule_after: set[TalkID] = field(default_factory=set)
 
 
 class SlotMachine(object):
@@ -87,6 +88,34 @@ def active(self, slot: Slot, talk_id: TalkID, venue: VenueID) -> pulp.LpVariable
         self.var_cache[name] = variable
         return variable
 
+    def start_slot(self, talk_id: TalkID) -> pulp.LpVariable:
+        """A variable that is the number of the slot that talk ID is scheduled to begin."""
+        name = "S_start_%d" % (talk_id,)
+        if name in self.var_cache:
+            return self.var_cache[name]
+
+        variable = pulp.LpVariable(name, cat="Integer")
+        definition = pulp.lpSum(
+            self.start_var(slot, talk_id, venue) * slot
+            for slot in self.talks_by_id[talk_id].allowed_slots
+            for venue in self.talks_by_id[talk_id].venues
+        )
+        self.problem.addConstraint(variable == definition)
+        self.var_cache[name] = variable
+        return variable
+
+    def end_slot(self, talk_id: TalkID) -> pulp.LpVariable:
+        """A variable that is the number of the slot that talk ID is scheduled to begin."""
+        name = "S_end_%d" % (talk_id,)
+        if name in self.var_cache:
+            return self.var_cache[name]
+
+        variable = pulp.LpVariable(name, cat="Integer")
+        definition = self.start_slot(talk_id) + self.talks_by_id[talk_id].duration
+        self.problem.addConstraint(variable == definition)
+        self.var_cache[name] = variable
+        return variable
+
     def get_problem(
         self, venues: set[VenueID], talks: list[Talk], old_talks: list[OldTalk]
     ) -> pulp.LpProblem:
@@ -107,6 +136,13 @@ def get_problem(
                 == 1
             )
 
+        # Talks which must precede other talks do that
+        for talk in talks:
+            for schedule_before in talk.must_schedule_after:
+                self.problem.addConstraint(
+                    self.end_slot(schedule_before) <= self.start_slot(talk.id)
+                )
+
         # At most one talk may be active in a given venue and slot.
         for v in venues:
             for slot in self.slots_available:
diff --git a/tests/test_slotmachine.py b/tests/test_slotmachine.py
index e026546..50eb88f 100644
--- a/tests/test_slotmachine.py
+++ b/tests/test_slotmachine.py
@@ -24,6 +24,7 @@ def talk(
     venues: list[int],
     speakers: list[str],
     slots: Iterable[Slot] | Iterable[int],
+    must_schedule_after: list[int] = [],
 ) -> Talk:
     return Talk(
         id=TalkID(id),
@@ -31,6 +32,7 @@ def talk(
         venues={VenueID(vid) for vid in venues},
         speakers=speakers,
         allowed_slots={Slot(s) for s in slots},
+        must_schedule_after={TalkID(t) for t in must_schedule_after},
     )
 
 
@@ -253,3 +255,41 @@ def test_talk_clash(self):
 
         # Talk 1 must now be in slot 3 or 4
         self.assertIn(talks_slots[1], [3, 4])
+
+    def test_must_schedule_after(self):
+        avail_slots = SlotMachine.calculate_slots(
+            parser.parse("2016-08-06 13:00"),
+            parser.parse("2016-08-06 13:00"),
+            parser.parse("2016-08-06 15:00"),
+        )
+        _talk = partial(talk, slots=avail_slots[:], venues=[101])
+        talk_defs = [
+            _talk(
+                id=1, duration=3 + 1, speakers=["Speaker 1"], must_schedule_after=[2]
+            ),
+            _talk(
+                id=2, duration=2 + 1, speakers=["Speaker 2"], must_schedule_after=[3]
+            ),
+            _talk(
+                id=3, duration=2 + 1, speakers=["Speaker 3"], must_schedule_after=[4]
+            ),
+            _talk(id=4, duration=2 + 1, speakers=["Speaker 4"]),
+        ]
+        old_talks = [(0, 1, 101), (3, 2, 101), (6, 3, 101), (9, 4, 101)]
+        solved = self.schedule_and_basic_asserts(
+            talk_defs, avail_slots, old_talks=old_talks
+        )
+
+        slots, talks, venues = unzip(solved)
+        talks_slots = dict(zip(talks, slots))
+
+        # The talks are now in the reverse order of the one they were in in old_talks.
+        self.assertEqual(
+            {
+                4: 0,
+                3: 3,
+                2: 6,
+                1: 9,
+            },
+            talks_slots,
+        )