diff --git a/app/vmselect/prometheus/prometheus.go b/app/vmselect/prometheus/prometheus.go
index a244f13b9..67a2a955c 100644
--- a/app/vmselect/prometheus/prometheus.go
+++ b/app/vmselect/prometheus/prometheus.go
@@ -549,6 +549,14 @@ func getTime(r *http.Request, argKey string, defaultValue int64) (int64, error)
 		// Try parsing string format
 		t, err := time.Parse(time.RFC3339, argValue)
 		if err != nil {
+			// Handle Prometheus'-provided minTime and maxTime.
+			// See https://github.com/prometheus/client_golang/issues/614
+			switch argValue {
+			case prometheusMinTimeFormatted:
+				return minTimeMsecs, nil
+			case prometheusMaxTimeFormatted:
+				return maxTimeMsecs, nil
+			}
 			return 0, fmt.Errorf("cannot parse %q=%q: %s", argKey, argValue, err)
 		}
 		secs = float64(t.UnixNano()) / 1e9
@@ -560,6 +568,13 @@ func getTime(r *http.Request, argKey string, defaultValue int64) (int64, error)
 	return msecs, nil
 }
 
+var (
+	// These constants were obtained from https://github.com/prometheus/prometheus/blob/91d7175eaac18b00e370965f3a8186cc40bf9f55/web/api/v1/api.go#L442
+	// See https://github.com/prometheus/client_golang/issues/614 for details.
+	prometheusMinTimeFormatted = time.Unix(math.MinInt64/1000+62135596801, 0).UTC().Format(time.RFC3339Nano)
+	prometheusMaxTimeFormatted = time.Unix(math.MaxInt64/1000-62135596801, 999999999).UTC().Format(time.RFC3339Nano)
+)
+
 const (
 	// These values prevent from overflow when storing msec-precision time in int64.
 	minTimeMsecs = int64(-1<<63) / 1e6
diff --git a/app/vmselect/prometheus/prometheus_test.go b/app/vmselect/prometheus/prometheus_test.go
new file mode 100644
index 000000000..a4a5cb517
--- /dev/null
+++ b/app/vmselect/prometheus/prometheus_test.go
@@ -0,0 +1,78 @@
+package prometheus
+
+import (
+	"fmt"
+	"testing"
+	"net/http"
+	"net/url"
+)
+
+func TestGetTimeSuccess(t *testing.T) {
+	f := func(s string, timestampExpected int64) {
+		t.Helper()
+		urlStr := fmt.Sprintf("http://foo.bar/baz?s=%s", url.QueryEscape(s))
+		r, err := http.NewRequest("GET", urlStr, nil)
+		if err != nil {
+			t.Fatalf("unexpected error in NewRequest: %s", err)
+		}
+
+		// Verify defaultValue
+		ts, err := getTime(r, "foo", 123)
+		if err != nil {
+			t.Fatalf("unexpected error when obtaining default time from getTime(%q): %s", s, err)
+		}
+		if ts != 123 {
+			t.Fatalf("unexpected default value for getTime(%q); got %d; want %d", s, ts, 123)
+		}
+
+		// Verify timestampExpected
+		ts, err = getTime(r, "s", 123)
+		if err != nil {
+			t.Fatalf("unexpected error in getTime(%q): %s", s, err)
+		}
+		if ts != timestampExpected {
+			t.Fatalf("unexpected timestamp for getTime(%q); got %d; want %d", s, ts, timestampExpected)
+		}
+	}
+
+	f("2019-07-07T20:01:02Z", 1562529662000)
+	f("2019-07-07T20:47:40+03:00", 1562521660000)
+	f("-292273086-05-16T16:47:06Z", -9223372036854)
+	f("292277025-08-18T07:12:54.999999999Z", 9223372036854)
+	f("1562529662.324", 1562529662324)
+	f("-9223372036.854", -9223372036854)
+}
+
+func TestGetTimeError(t *testing.T) {
+	f := func(s string) {
+		t.Helper()
+		urlStr := fmt.Sprintf("http://foo.bar/baz?s=%s", url.QueryEscape(s))
+		r, err := http.NewRequest("GET", urlStr, nil)
+		if err != nil {
+			t.Fatalf("unexpected error in NewRequest: %s", err)
+		}
+
+		// Verify defaultValue
+		ts, err := getTime(r, "foo", 123)
+		if err != nil {
+			t.Fatalf("unexpected error when obtaining default time from getTime(%q): %s", s, err)
+		}
+		if ts != 123 {
+			t.Fatalf("unexpected default value for getTime(%q); got %d; want %d", s, ts, 123)
+		}
+
+		// Verify timestampExpected
+		ts, err = getTime(r, "s", 123)
+		if err == nil {
+			t.Fatalf("expecting non-nil error in getTime(%q)", s)
+		}
+	}
+
+	f("foo")
+	f("2019-07-07T20:01:02Zisdf")
+	f("2019-07-07T20:47:40+03:00123")
+	f("-292273086-05-16T16:47:07Z")
+	f("292277025-08-18T07:12:54.999999998Z")
+	f("-9223372036.855")
+	f("9223372036.855")
+}