This paper examines the rheological behaviour of power law viscous materials arising from mixtures of deformation mechanisms and/or different mineral assemblages. The mixing relation is based on classical thermodynamics mixing relations where the enthalpy of the mixture is the sum of the molar volume proportions of the individual molar enthalpies; this is equivalent to the 1887 Arrhenius mixing relation for Newtonian viscosities. We compare this mixing relation to viscosities obtained from finite element simulations of deforming mixed mineral phases and from experimental results. The mixing relation helps understanding of apparent anomalies in experimental results for calcite and quartz. This then enables the construction of flow laws and of deformation mechanism maps for mixtures of deformation mechanisms and of mineral assemblages over a range of grain size distributions. The rheological implications for changes in the topology (such as anisotropy) of mineral arrangements, for mixtures of grain sizes, for the interpretation of experimental results and for geodynamic modelling are discussed.