The photograph above left shows an Imperial Cockade worn on an other ranks tropical helmet of the Cavalry Squadron of the East Asian Occupation Brigade.
Photo by C Dale at the Internationales Maritimes Museum, Hamburg

The photograph above centre shows an Imperial Cockade worn on an other ranks field cap from of a Marine Infantry Seebataillon.
Photo © Doppler Collection

The photograph above right shows an Imperial Cockade worn on an other ranks Südwester from the South West African Schutztruppe. Note that the white painted ring has almost entirely worn off.
Photo © Doppler Collection

The photograph above left shows an Imperial Cockade worn on the Südwester of an officer of the South West African Schutztruppe. Note the higher quality pressing with a more elaborate design and that the white ring is shown with polished white metal. This example is from .
Photo © Doppler Collection

The photograph above centre shows an Imperial Cockade worn on the Südwester of an NCO of the South West African Landespolizei. Note the raised white metal ring and red felt centre typical of private purchase cockades. This example is from an officers Südwester of the South West African Landespolizei.
Photo © Doppler Collection

The photograph above right shows an Imperial Cockade worn on the Südwester of senior NCOs in the South West African Schutztruppe. Note that the paint has largely worn off sections of the cockade and that the white ring is replaced with polished white metal, also note the effect of a smaller cockade within the larger. 
Photo © Doppler Collection

Large serrated imperial cockades were also worn under the right side chinstrap boss of the Pickelhaube and Jäger-style shako, when these items were worn. The spiked helmet or Pickelhaube was worn by East African Schutztruppe on home duties between 1891-96 and by East Asian troops. The Jäger -style shako was worn by East Asian Jäger and train troops and by the Marine Infantry. Removable oval cockades were also worn on the front of Jäger-style shakos.

The photograph above left shows an other ranks imperial cockade worn under the right hand side chinstrap boss of a Pickelhaube. This example is from a helmet from the Alsace-Lorraine Gendarmerie.
Photo © Adrien M

The photograph above centre shows a Pioneer officers Pickelhaube and a train other ranks shako of the East Asian Occupation Brigade. Note the oval cockade on the top front of the shako and the cockade under the chinstrap boss of the Pickelhaube. This Pickelhaube being an officer's helmet has a raised white metal ring.
Photo © Mark Schellenberg at the Internationales Maritimes Museum, Hamburg

The photograph above right shows an oval cockade worn on a Marine Infantry shako. Note the additional ring of white between the black and red sections used on the oval version of the imperial cockade. Officers oval imperial cockades had the white sections in white metallic lace and another white section inside the red centre. Oval state cockades were usually abbreviated into two colours, for example: white/black for Prussia, white/blue for Bavaria, white/green for Saxony etc..
Photo by C Dale at the Musée Royale de l'Armée Collection, Brussels

Units such as the Imperial Navy (including the Marine Infantry), the Schutztruppe (and colonial police) and the East Asian Occupation Brigade from 1901, were under direct Imperial command and therefore only wore the single Imperial cockade.

The Imperial German army back home was made up of units from the different German kingdoms and duchies (Prussia, Bavaria, Saxony etc). In addition to the imperial cockade they wore their state cockade in different national colours on their headdress.

Overseas units that did wear both imperial and state cockades included the East Asian Expeditionary Corps (until 1901), the Georgian Mission (most of whom were Bavarian), the Pascha Expeditions and other German army units posted to the Ottoman Empire. In addition individual army officers seconded from their home units to the Schutztruppe or other overseas service retained their home unit's state cockade.

These state cockades were worn below the imperial cockade on the field cap, Südwester and East Asian Expeditionary Corps straw hat. On the Pickelhaube and Jäger-style shako they were worn under the left hand side chinstrap boss. On Jäger-style shakos they also replaced the oval cockade worn on the front where applicable. The different colours for state cockades are illustrated below.

The photograph above left shows an imperial cockade above a Hamburg cockade worn on a the tropical helmet of an officer of the 76th Hamburg Infantry Regiment seconded to the colonies.
Photo © Mark Schellenberg at the Internationales Maritimes Museum, Hamburg
Photo ©

The photograph above centre shows an imperial cockade above a Schwarzburg-Sonderhausen cockade on a 1900 straw hat from the East Asian Expeditionary Corps. The tiny Principality of Schwarzburg-Sonderhausen (white/blue/white cockade, confusingly similar to the white/pale blue/white of Bavaria) only contributed one battalion of infantry to the imperial army, namely the III. Battalion of the 71st Thuringian Infantry Regiment. And only one officer from that battalion served in the East Asian Expeditionary Corps, thus enabling us to identify this unique hat as belonging to Leutnant von Stockhausen.
Photo © Mark Schellenberg at the Internationales Maritimes Museum, Hamburg

The photograph above right left shows an imperial cockade above a Prussian reserve cockade worn on a Südwester of a pharmacist of the Schutztruppe. The owner of this hat was a seconded Prussian reserve officer, hence the addition of the Prussian officers cockade with a reserve cross on it.
Photo © Mark Schellenberg at the Internationales Maritimes Museum, Hamburg