A new technique for estimating market power in several markets simultaneously is developed and applied to the Australian retail beef, lamb, and pork markets. The hypotheses that market power is zero and that market power is the same for each meat cannot be rejected. Nor is there evidence that market power increased over the period of analysis. Little bias is created by examining markets in isolation, rather than within a system, when markets are competative, but that bias can be large when market power exists in some markets in the system.