The complete homogeneous form of the quantum mechanical master equation for a heteronuclear two-spin system is presented in the basis of Cartesian product operators. The homogeneous master equation is useful since it allows fast, single-step computation of the density operator during pulse sequences, without neglecting relaxation effects. The homogeneous master equation is also a prerequisite for an expansion of the average Hamiltonian theory to include relaxation, thus forming average Liouvillian theory. The coherences of the two-spin system are assumed to be relaxed both by mutual dipole-dipole interaction and by chemical shift anisotropy interaction with the static magnetic field. The cross-correlation between dipole-dipole and chemical shift anisotropy relaxation mechanisms is also considered. To illustrate the applicability of the developed formalism we simulate the overall transfer efficiency of three different inverse detection 1H-15N correlation experiments with parameters corresponding to a large protein. Copyright 1998 Academic Press.