Experimental evidence indicates that tissue interaction plays an essential role during skin pattern formation. Here we focus on the mathematical aspects of two specific tissue interaction models. Introducing interaction mechanisms into the traditional pattern formation models is not only biologically consistent, but also leads to results agreeing more closer to those observed in embryogenesis. We specifically examine the bifurcations from spatially simple solutions to spatially complex patterns. In both models this increased complexity in solution is obtained by increasing the effect of the interaction mechanism through a certain threshold. The role of tissue interaction in sequential patterning is also considered.