A detailed study of the cross-relaxation effects between the H-1 and H-2 spins systems is presented in the nematic phase of a 5-cyanobiphenyl (5CB) liquid crystal, partially deuterated at alpha position (5CB-alpha d(2)). The proton spin-lattice relaxation time was measured at a frequency range from 5 kHz to 100 MHz at a temperature 5 K below the nematic-isotropic phase transition. In the low frequency domain, the spin-lattice relaxation rate (T-1(-1)) dispersion clearly differs from that of the fully protonated 5CB homologue. At two distinct frequencies, T-1(-1) presents two distinct local maxima and for low frequencies T-1(-1) presents a stronger frequency dependence when compared with what is observed for 5CB. The T-1(-1) dispersion obtained for 5CB-alpha d(2) for frequencies above 60 kHz was interpreted in terms of the relaxation mechanisms usually accepted to interpret the spin-lattice relaxation in nematic phases in general and 5CB in particular. For lower frequencies it was necessary to consider cross-relaxation contributions between the proton and deuterium reservoirs. A detailed model interpretation of the deuterium quadrupolar dips with respect to the proton-spin relaxation is presented. The analysis of the quadrupolar relaxation independently confirms that the order director fluctuations is the dominant mechanism of proton relaxation in the low frequency domain.