diff --git a/src/index.js b/src/index.js
index 061ade178..27c393ded 100644
--- a/src/index.js
+++ b/src/index.js
@@ -151,13 +151,27 @@ class Dayjs {
         Date.UTC(this.$y, m, d) : new Date(this.$y, m, d), this)
       return isStartOf ? ins : ins.endOf(C.D)
     }
-    const instanceFactorySet = (method, slice) => {
+    const instanceFactorySet = (method, slice, keepOffset) => {
       const argumentStart = [0, 0, 0, 0]
       const argumentEnd = [23, 59, 59, 999]
-      return Utils.w(this.toDate()[method].apply( // eslint-disable-line prefer-spread
-        this.toDate('s'),
+      const date = this.toDate('s')
+      // In UTC mode the setters are setUTC* and no wall clock is ambiguous.
+      const trackOffset = keepOffset && !this.$u
+      const oldOffset = trackOffset ? date.getTimezoneOffset() : 0
+      const time = this.toDate()[method].apply( // eslint-disable-line prefer-spread
+        date,
         (isStartOf ? argumentStart : argumentEnd).slice(slice)
-      ), this)
+      )
+      if (!trackOffset) return Utils.w(time, this)
+      // A Date setter resolves the wall clock that repeats at a DST fall back to
+      // its first occurrence, moving the result a whole offset step away from the
+      // instant it came from. Units below a day never leave the offset they
+      // started in, so pull the result back when that offset still holds there.
+      const newOffset = date.getTimezoneOffset()
+      const shifted = time + ((oldOffset - newOffset) * C.MILLISECONDS_A_MINUTE)
+      const keep = oldOffset === newOffset ||
+        new Date(shifted).getTimezoneOffset() === oldOffset
+      return Utils.w(keep ? shifted : time, this)
     }
     const { $W, $M, $D } = this
     const utcPad = `set${this.$u ? 'UTC' : ''}`
@@ -177,11 +191,11 @@ class Dayjs {
       case C.DATE:
         return instanceFactorySet(`${utcPad}Hours`, 0)
       case C.H:
-        return instanceFactorySet(`${utcPad}Minutes`, 1)
+        return instanceFactorySet(`${utcPad}Minutes`, 1, true)
       case C.MIN:
-        return instanceFactorySet(`${utcPad}Seconds`, 2)
+        return instanceFactorySet(`${utcPad}Seconds`, 2, true)
       case C.S:
-        return instanceFactorySet(`${utcPad}Milliseconds`, 3)
+        return instanceFactorySet(`${utcPad}Milliseconds`, 3, true)
       default:
         return this.clone()
     }
diff --git a/test/timezone.test.js b/test/timezone.test.js
index 42cab8934..fd83e07b9 100644
--- a/test/timezone.test.js
+++ b/test/timezone.test.js
@@ -80,3 +80,35 @@ it('UTC diff in DST', () => {
   expect(day1.diff(day2, 'd'))
     .toBe(-3)
 })
+
+// The wall clock right after a fall back is the one that just happened, so the
+// Date setters startOf/endOf rely on can resolve it to the earlier offset and
+// drop the result a whole hour. Only one hour fall backs are collected, so that
+// the repeated wall clock covers a whole hour; a host without DST yields none.
+const fallBacks = () => {
+  const result = []
+  let previous = new Date(Date.UTC(2015, 0, 1)).getTimezoneOffset()
+  for (let t = Date.UTC(2015, 0, 1); t < Date.UTC(2030, 0, 1); t += 3600000) {
+    const offset = new Date(t).getTimezoneOffset()
+    if (offset - previous === 60) result.push(t) // the clock was moved back here
+    previous = offset
+  }
+  return result
+}
+
+it('startOf/endOf below a day in a repeated hour (DST)', () => {
+  fallBacks().forEach((transition) => {
+    const time = transition + (15 * 60 * 1000) + 45123 // inside the repeated hour
+    const dayjsTest = dayjs(time)
+    const momentTest = moment(time);
+    ['hour', 'minute', 'second'].forEach((unit) => {
+      expect(dayjsTest.startOf(unit).valueOf()).toBe(momentTest.clone().startOf(unit).valueOf())
+      expect(dayjsTest.endOf(unit).valueOf()).toBe(momentTest.clone().endOf(unit).valueOf())
+      expect(dayjsTest.isSame(dayjsTest, unit)).toBe(true)
+    })
+    // startOf only clears the fields below its unit, it never moves the clock
+    expect(time - dayjsTest.startOf('second').valueOf()).toBe(dayjsTest.millisecond())
+    expect(time - dayjsTest.startOf('minute').valueOf())
+      .toBe((dayjsTest.second() * 1000) + dayjsTest.millisecond())
+  })
+})