An ink container for an ink jet print head has a main tank filled with an absorbent fibrous material which holds ink by capillary action. A feed channel conducts ink from the main tank to a feed chamber whence it passes to the head. An auxiliary tank (30) is fixed to the side of the main tank (15) and communicates with it by a channel at the end of the main tank having the feed channel. The container can be refilled by inserting ink through an aperture into the auxiliary tank from where it passes into the main tank by capillary action.