Electron spin relaxation for an S=1 system and its field dependence in the presence of static zero-field splitting (ZFS) has been described and incorporated in a model for nuclear spin-lattice relaxation in paramagnetic complexes in solution, proposed earlier by the group in Florence. Slow reorientation is assumed and the electron spin energy level structure (at any orientation of the molecule with respect to the laboratory frame) is described in terms of the Zeeman interaction and of the static ZFS. The electron spin relaxation is assumed to be caused by a transient ZFS modulated by the deformation of the complex described as a distortional (or pseudorotational) motion and the Redfield theory is used to derive the electron spin relaxation matrices. In the description of the electron spin relaxation we neglect any contribution from mechanisms involving modulation by reorientation, such as those of the static ZFS and the less important Zeeman interaction, as we limit ourselves to the slow-rotation limit (i.e., tau(R)much greater than tau(S)). This in general covers the behavior of proteins and macromolecules. The decomposition (DC) approximation is used, which means that the reorientational motion and electron spin dynamics are assumed to be uncorrelated. This is not a serious problem, due to the slow-rotation condition, since reorientational and distortional motions are time-scale separated. The resulting nuclear magnetic relaxation dispersion (NMRD) profiles obtained using the Florence model are calculated and compared with the calculations of the Swedish approach, which can be considered essentially exact within the given set of assumed interactions and dynamic processes. That theory is not restricted by the Redfield limit and can thus handle electron spin relaxation in the slow-motion regime, which is a consequence of not explicitly defining any electron spin relaxation times. Furthermore, the DC approximation is not invoked, and in addition, the electron spin relaxation is described by reorientationally modulated static ZFS and Zeeman interaction besides the distortionally modulated transient ZFS. The curves computed with the Florence model show a satisfactory agreement with these more accurate calculations of the Swedish approach, in particular for the axially symmetric static ZFS tensor, providing confidence in the adequacy of the electron spin relaxation model under the condition of slow rotation. The comparison is also quite instructive as far as the physical meaning of the electron spin relaxation and of its interplay with the nuclear spin system are concerned.