Theories for deformation of polycrystals have been substantially refined, enabling us to model deformation of metals and minerals with considerable sophistication. So far, most modelling has been confined to single-phase aggregates such as quartzite and limestone. We present the first results for a polyphase aggregate, peridotite, consisting of 70% olivine and 30% enstatite. The problem is approached with a viscoplastic self-consistent theory satisfying stress equilibrium and strain compatibility for the average polycrystal and taking account of anistropic neighbor interactions. It is assumed that olivine deforms by (010)<100>, (001)<100>, and (010)<001> slip and enstatite deforms by (100)<001> slip. Simulated textures for olivine and enstatite in peridotite resemble simulated textures in the pure phases, indicating that for this system and for these volume fractions there is little influence of the different phases upon each other. In our model the harder mineral enstatite deforms at a slower rate than olivine. Interaction between neighboring grains appears to be minimal, which may be due to model assumptions. Predicted pole figures with olvine (010) axes and enstatite (100) axes aligning with the direction of shortening are in good agreement with preferred orientations in naturally and experimentally deformed peridotites. ¿American Geophysical Union 1991