The Gelmke is a small stream, roughly 6 kilometres (3.7 mi) long, and right-hand tributary of the Abzucht in Lower Saxony, Germany.

The stream flows through part of the town of Goslar.

Its source lies east-northeast of the hill known as the Dicker Kopf (668 m) and north of the Eichenberg (670 m).

[2] It flows initially northwards through a densely wooded valley, where it is crossed by the E 11 European long-distance trail before emerging into open fields and swinging east, just above the old Goslar sewage ponds.

It then heads north again to join the Abzucht near Goslar station.