SUMMARY: A dynamic Monte Carlo (MC) simulation is performed to investigate the phase behavior of mixtures of flexible polymers and low molecular weight thermotropic liquid crystals (LCs). The polymer is represented by three-dimensional self-avoiding lattice chains, while the LC is described by the LebwohlLasher nematogen model. The initially homogeneous rod-coil mixture is, following a deep quench, separated into an isotropic phase rich in coils and a nematic phase rich in rods. The underlying spinodal decomposition (SD) process is then simulated and studied extensively. This is the first simulation of SD in a rod-coil mixture where the nematic ordering is included. Concentration fluctuations with a conserved order parameter are thus coupled with orientation fluctuations with a nonconserved order parameter. It is found that the early stage SD in the rod-coil mixture still exhibits the dominant spatial wavelength and that the scalar scattering functions in the late stage of SD obey the Furukawa scaling law. The kinetic difference between the so-called isotropic and anisotropic SD regions is, however, much less pronounced than predicted recently by the mean-field theory.