In the present study we consider a general algebraically tractable approach to the construction of lattice-Boltzmann (LB) schemes for the simulation of non-Newtonian and two-phase flows. The chain of moment equations is truncated at a level corresponding to the rheology of the liquid, and is closed by a Chapman–Enskog procedure. The collision term of the LB method is linked to the second moment of the velocity distribution via the constitutive equation of the liquid. The resulting nonlinear algebraic equation can be efficiently solved for an arbitrary rheological law. The algorithm can be extended to a two-phase system.