We report Coulomb drag measurements on GaAs-AlGaAs electron-hole bilayers. The two layers are separated by a 10 or 25nm barrier. Below T≈1K we find two features that a Fermi-liquid picture cannot explain. First, the drag on the hole layer shows an upturn, which may be followed by a downturn. Second, the effect is either absent or much weaker in the electron layer, even though the measurements are within the linear response regime. Correlated phases have been anticipated in these, but surprisingly, the experimental results appear to contradict Onsager's reciprocity theorem.

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