The spin dynamics of paramagnets with uniaxial and exchange anisotropy is investigated in the high-temperature limit. For a Hamiltonian consisting of both an anisotropic exchange and a uniaxial anisotropy interaction, lowest-order integral equations for the dynamical two-point correlation functions are derived by means of a previously developed infinite-temperature diagrammatic technique. These equations are valid for all values of the spin quantum number S and for all values of the ratio DJ, where D is the uniaxial anisotropy energy and J is an exchange energy. A systematic study of the numerical solutions to these equations is then made as a function of both S and R=3D216S(S+1)J2 for 1≤S≤52 and for 0.0≤R≤5.0. In particular, the "local" spectral functions, the spin diffusion coefficients, and the exchange-narrowed dipolar linewidths are studied as a function of these parameters. The latter quantities are measurable in neutron scattering and EPR experiments in magnetic insulators. Finally, the diffusion coefficients and dipolar linewidths are evaluated for the uniaxial paramagnets NiF2, CoF2, FeF2, and MnF2, and the experimental implications of these results are discussed.