Adhesive organs on the legs of arthropods and vertebrates are strongly direction dependent, making contact only when pulled towards the body but detaching when pushed away from it. Here we show that the two types of attachment pads found in cockroaches (Nauphoeta cinerea), tarsal euplantulae and pretarsal arolium, serve fundamentally different functions. Video recordings of vertical climbing revealed that euplantulae are almost exclusively engaged with the substrate when legs are pushing, whereas arolia make contact when pulling. Thus, upward-climbing cockroaches used front leg arolia and hind leg euplantulae, whereas hind leg arolia and front leg euplantulae were engaged during downward climbing. Single-leg friction force measurements showed that the arolium and euplantulae have an opposite direction dependence. Euplantulae achieved maximum friction when pushed distally, whereas arolium forces were maximal during proximal pulls. This direction dependence was not explained by the variation of shear stress but by different contact areas during pushing or pulling. The changes in contact area result from the arrangement of the flexible tarsal chain, tending to detach the arolium when pushing and to peel off euplantulae when in tension. Our results suggest that the euplantulae in cockroaches are not adhesive organs but 'friction pads', mainly providing the necessary traction during locomotion.