The work presented in this thesis is a theoretical and numerical investigation of the spin- dynamics in two recently demonstrated experiments involving long periods of RF irradiation on the quadrupolar nuclei channel, the 1 H - 14N double cross polarization (double CP) under fast MAS experiment by Carnevale et al. and the 1H - 35Cl TRAPDOR-HMQC experiment of Hung et al. Creation and evolution of various coherences generated in these proton-detected experiments are explored. To analyse the rich and complex spin dynamics due to the interference between the large time-dependent quadrupolar interaction and the radio-frequency (RF) field, an exact effective Hamiltonian is constructed numerically using the matrix logarithm approach. Structure of the effective Hamiltonian is connected with transfer amplitudes to various coherences, the output signal, etc. and, when possible, features of the spin dynamics are derived theoretically. The analysis also provides insight on the efficiency of these experiments under different experimental conditions.