We address the question of using a lattice gas method to study flows of complex fluids, such as non‐Newtonian or miscible fluids. A Bhatnagar, Gross, and Krook lattice technique provides a tool to simulate the flow of one fluid and the diffusion of a tracer in that fluid. We extend the technique to flows in which the viscosity is space and time dependent. This approach is suitable for non‐Newtonian fluids (shear dependent viscosity) and miscible fluids (concentration dependent viscosity). The modified scheme is tested on physical flow situations, analytically tractable for the sake of comparison. ©1996 American Institute of Physics.