A numeric algorithm which is suitable for calcg. lineshapes of cross-polarization spectra influenced by isotropic and anisotropic tumbling is proposed. It is based on a description of the cross-polarization process using single-transition operators combined with rotational diffusion represented by a stationary Markov operator. A corresponding Fortran program can be implemented on a regular personal computer. The calcns. yield spectral lineshapes for various mixing times under given cross-polarization conditions which reflect the characteristics of mol. motion. Representative results show typical transient oscillations on powder spectra, the dependence of the lineshapes on the degree of mobility, the effects of sample spinning, the consequence of a given deviation from the Hartmann-Hahn condition, and the effect of addnl. dipolar coupling between I spins. The applicability of the algorithm is demonstrated on supercooled glycerol as a model system. (c) 2000 Academic Press.