diff --git a/test/intl402/Temporal/ZonedDateTime/prototype/hoursInDay/same-date-starts-twice.js b/test/intl402/Temporal/ZonedDateTime/prototype/hoursInDay/same-date-starts-twice.js
new file mode 100644
index 0000000000..743dd3be44
--- /dev/null
+++ b/test/intl402/Temporal/ZonedDateTime/prototype/hoursInDay/same-date-starts-twice.js
@@ -0,0 +1,19 @@
+// Copyright (C) 2024 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.zoneddatetime.prototype.hoursinday
+description: Handles dates with offset transitions where midnight occurs twice.
+features: [Temporal]
+---*/
+
+// Test date with offset transition where the same day starts twice
+// See https://github.com/tc39/proposal-temporal/issues/2938 for more details
+
+const zdt1 = Temporal.ZonedDateTime.from('2010-11-06T00:00:00-02:30[America/St_Johns]');
+const zdt2 = Temporal.ZonedDateTime.from('2010-11-07T23:00:00-03:30[America/St_Johns]');
+const zdt3 = Temporal.ZonedDateTime.from('2010-11-08T23:00:00-03:30[America/St_Johns]');
+
+assert.sameValue(zdt1.hoursInDay, 24);
+assert.sameValue(zdt2.hoursInDay, 25);
+assert.sameValue(zdt3.hoursInDay, 24);
diff --git a/test/intl402/Temporal/ZonedDateTime/prototype/startOfDay/same-date-starts-twice.js b/test/intl402/Temporal/ZonedDateTime/prototype/startOfDay/same-date-starts-twice.js
new file mode 100644
index 0000000000..1a43cc0a3f
--- /dev/null
+++ b/test/intl402/Temporal/ZonedDateTime/prototype/startOfDay/same-date-starts-twice.js
@@ -0,0 +1,23 @@
+// Copyright (C) 2024 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+esid: sec-temporal.zoneddatetime.prototype.startofday
+description: Handles dates with offset transitions where midnight occurs twice.
+includes: [temporalHelpers.js]
+features: [Temporal]
+---*/
+
+// Test date with offset transition where the same day starts twice
+// See https://github.com/tc39/proposal-temporal/issues/2938 for more details
+
+const zdt1 = Temporal.ZonedDateTime.from('2010-11-06T00:00:00-02:30[America/St_Johns]');
+const zdt2 = Temporal.ZonedDateTime.from('2010-11-07T23:00:00-03:30[America/St_Johns]');
+const zdt3 = Temporal.ZonedDateTime.from('2010-11-08T23:00:00-03:30[America/St_Johns]');
+
+const startOfDay2 = Temporal.ZonedDateTime.from('2010-11-07T00:00:00-02:30[America/St_Johns]');
+const startOfDay3 = Temporal.ZonedDateTime.from('2010-11-08T00:00:00-03:30[America/St_Johns]');
+
+TemporalHelpers.assertZonedDateTimesEqual(zdt1.startOfDay(), zdt1);
+TemporalHelpers.assertZonedDateTimesEqual(zdt2.startOfDay(), startOfDay2);
+TemporalHelpers.assertZonedDateTimesEqual(zdt3.startOfDay(), startOfDay3);