diff --git a/types.go b/types.go
index 2c647fd2..ac8e140e 100644
--- a/types.go
+++ b/types.go
@@ -53,9 +53,23 @@ func (date NumericDate) MarshalJSON() (b []byte, err error) {
 	if TimePrecision < time.Second {
 		prec = int(math.Log10(float64(time.Second) / float64(TimePrecision)))
 	}
-	f := float64(date.Truncate(TimePrecision).UnixNano()) / float64(time.Second)
-
-	return []byte(strconv.FormatFloat(f, 'f', prec, 64)), nil
+	truncatedDate := date.Truncate(TimePrecision)
+
+	// For very large timestamps, UnixNano would overflow an int64, but this
+	// function requires nanosecond level precision, so we have to use the
+	// following technique to get round the issue:
+	// 1. Take the normal unix timestamp to form the whole number part of the
+	//    output,
+	// 2. Take the result of the Nanosecond function, which retuns the offset
+	//    within the second of the particular unix time instance, to form the
+	//    decimal part of the output
+	// 3. Concatenate them to produce the final result
+	seconds := strconv.FormatInt(truncatedDate.Unix(), 10)
+	nanosecondsOffset := strconv.FormatFloat(float64(truncatedDate.Nanosecond())/float64(time.Second), 'f', prec, 64)
+
+	output := append([]byte(seconds), []byte(nanosecondsOffset)[1:]...)
+
+	return output, nil
 }
 
 // UnmarshalJSON is an implementation of the json.RawMessage interface and deserializses a
diff --git a/types_test.go b/types_test.go
index bc28605a..b26c2bef 100644
--- a/types_test.go
+++ b/types_test.go
@@ -2,6 +2,7 @@ package jwt_test
 
 import (
 	"encoding/json"
+	"math"
 	"testing"
 	"time"
 
@@ -79,23 +80,38 @@ func TestNumericDate_MarshalJSON(t *testing.T) {
 	}{
 		{time.Unix(5243700879, 0), "5243700879", time.Second},
 		{time.Unix(5243700879, 0), "5243700879.000", time.Millisecond},
-		{time.Unix(5243700879, 0), "5243700879.000001", time.Microsecond},
-		{time.Unix(5243700879, 0), "5243700879.000000954", time.Nanosecond},
+		{time.Unix(5243700879, 0), "5243700879.000000", time.Microsecond},
+		{time.Unix(5243700879, 0), "5243700879.000000000", time.Nanosecond},
 		//
 		{time.Unix(4239425898, 0), "4239425898", time.Second},
 		{time.Unix(4239425898, 0), "4239425898.000", time.Millisecond},
 		{time.Unix(4239425898, 0), "4239425898.000000", time.Microsecond},
 		{time.Unix(4239425898, 0), "4239425898.000000000", time.Nanosecond},
 		//
+		{time.Unix(253402271999, 0), "253402271999", time.Second},
+		{time.Unix(253402271999, 0), "253402271999.000", time.Millisecond},
+		{time.Unix(253402271999, 0), "253402271999.000000", time.Microsecond},
+		{time.Unix(253402271999, 0), "253402271999.000000000", time.Nanosecond},
+		//
 		{time.Unix(0, 1644285000210402000), "1644285000", time.Second},
 		{time.Unix(0, 1644285000210402000), "1644285000.210", time.Millisecond},
 		{time.Unix(0, 1644285000210402000), "1644285000.210402", time.Microsecond},
-		{time.Unix(0, 1644285000210402000), "1644285000.210402012", time.Nanosecond},
+		{time.Unix(0, 1644285000210402000), "1644285000.210402000", time.Nanosecond},
 		//
 		{time.Unix(0, 1644285315063096000), "1644285315", time.Second},
 		{time.Unix(0, 1644285315063096000), "1644285315.063", time.Millisecond},
 		{time.Unix(0, 1644285315063096000), "1644285315.063096", time.Microsecond},
-		{time.Unix(0, 1644285315063096000), "1644285315.063096046", time.Nanosecond},
+		{time.Unix(0, 1644285315063096000), "1644285315.063096000", time.Nanosecond},
+		// Maximum time that a go time.Time can represent
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775807", time.Second},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775807.999", time.Millisecond},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775807.999999", time.Microsecond},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775807.999999999", time.Nanosecond},
+		// Strange precisions
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775807", time.Second},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854775756", time.Minute},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854774016", time.Hour},
+		{time.Unix(math.MaxInt64, 999999999), "9223372036854745216", 24 * time.Hour},
 	}
 
 	for i, tc := range tt {