[en] Nuclear magnetic resonance (NMR) experiments were carried out in two heavy fermion superconductors, CeCu₂Si₂ and U/sub 1-x/Th/sub x/Be₁₃ (x = 0,0.0331). The unusual normal state and superconducting state behavior of CeCu₂Si₂ and UBe₁₃ has recently been discovered. Both compounds exhibit enormous values of the normal state low temperature magnetic susceptibility chi and the linear specific heat coefficient γ. Standard analyses of chi and γ results in a two order of magnitude enhancement of the conduction electron mass, but the ratio chi/γ retains a value appropriate to a free-electron gas. It is of interest to obtain as much microscopic information as possible. In one of the CeCu₂Si₂ superconducting specimens, the observed temperature dependence of the spin-lattice relaxation rate 1/T₁ (T) is consistent with a conventional quasi-particle excitation spectrum below the superconducting transition temperature T/sub c/. In the other superconducting CeCu₂Si₂ sample, the nuclear spin-lattice relaxation rate decreases drastically just below T/sub c/ without the apparent enhancement observed in the first sample. The spin lattice relaxation rate in UBe₁₃ varies approximately as T³ well below the transition temperature T/sub c/., This behavior is consistent with a class of anisotropic pairing models for which the superconducting gap vanishes along lines on the Fermi surface