The effect of an offset term in the cross-polarization (CP) Hamiltonian of a heteronuclear spin-12 pair due to off-resonant radio frequency (rf) irradiation and/or chemical shift anisotropy on one of the rf channels is investigated. Analytical solutions, simulations, and experimental results are presented. Formulating the CP spin dynamics in terms of an explicit unitary evolution operator enables the CP period to be inserted as a module in a given pulse scheme regardless of the initial density matrix present. The outcome of post-CP manipulation via pulses can be calculated on the resulting density matrix as the phases and amplitudes of all coherence modes are available. Using these tools it is shown that the offset can be used to reduce the rf power on that channel and the performance is further improved by a post-CP pulse whose flip angle matches and compensates the tilt of the effective field on the offset channel. Experimental investigations on single crystalline and polycrystalline samples of peptides confirm the oscillatory nature of CP dynamics and prove the slowing down of the dynamics under offset and/or mismatch conditions.