A systematic study of the Raman spectra of Pb(Zr1-xTix)O-3 (PZT) ceramics has been performed in a broad temperature interval (10-600 K) and a broad Ti/Zr concentration range around the morphotropic phase boundary (x = 0.25-0.70). The number of the spectral components was estimated by a standard fitting procedure with damped harmonic oscillators as well as by counting the number of peaks and shoulders with the help of a purposely designed mathematical analysis based on frequency derivatives of the Raman spectra. This last method proves to be very useful to study Raman spectra of disordered materials. For the case of PZT, the comparison with the Raman modes of PbTiO3 allows us to assign the phonon bands on both sides of the morphotropic phase boundary, and the crossover from the tetragonal to rhombohedral phase spectra is clearly visible. However, there are no indications of a systematic splitting of the E-symmetry modes into monoclinic A'-A '' doublets in the morphotropic samples. Detailed adjusting of the response function to the spectrum requires to assume additional Raman-active modes, but this holds for a much broader concentration range than that of the anticipated monoclinic phase. In particular, the lowest frequency transverse optic mode of E-symmetry (soft mode of the ferroelectric phase transition) is split into two components, a THz frequency anharmonic (central modelike) component and a resonant component (at omega similar to 80 cm(-1)), both related to the same normal coordinate. The additional Raman band appearing in this frequency range (omega similar to 65 cm(-1)) at low temperatures is rather associated with the antiphase tilt vibrations of the oxygen octahedra.