Magnetic systems where the crystal-field ground state of the isolated ion is a singlet show no magnetic ordering for exchange small compared to crystal-field effects. We consider the effect of exchange as it increases from zero toward the critical value necessary for magnetic ordering with infinitesimal moment at T=0. In particular, we have calculated the susceptibility, nonlinear magnetization, and critical ratio of exchange to crystal-field splitting required for magnetic ordering for such systems, including exchange correlation effects by use of the constant coupling approximation. Substantial deviations from the molecularfield behavior are found at low temperatures as the exchange approaches the value required for magnetic ordering. Also we critically examine the pertinence of using boson spin-wave-like excitations to discuss thermodynamic properties in the paramagnetic case. While this formulation has certain inadequacies for treating such properties, this point of view could be quite valuable with regard to low-temperature inelastic neutron scattering experiments. Finally, the results are discussed with respect to the present experimental situation and with respect to the most promising line of investigation for future experiments.