Transverse nuclear spin relaxation experiments, employing the Carr-Purcell-Meiboom-Gill (CP) sequence, are analyzed under slow-motional conditions for deuterated probes experiencing order director fluctuations in nematic phases. The pulse-spacing dependent transverse relaxation rate is expressed as a function of all the viscoelastic parameters of the liquid crystal. The theory describes the effects of the anisotropy of the viscoelastic parameters on the dispersion profile beyond the commonly applied one-constant approximation.