The Hamiltonian constructed in a previous work in pseudo-spin space to explain the crystal-field effects in certain magnetic systems with various crystal-field level schemes has been studied in the random phase approximation of the double-time Green function method. By using the molecular field results obtained before as a second approximation, we obtain the low-lying collective excitation spectra at zero and finite temperatures. As an application, we have extended our calculations to look at the dispersion curves of the d.h.c.p. praseodymium single crystal. Comparison with the experimental measurements is discussed. Suggestions on further studies and possible improvements of the present calculations are also provided.