The longitudinal nuclear relaxation rates R(c,T) have been measured for the 115In and 209Bi nuclei in liquid alloys of IncSn1-c, BicSn1-c and IncPb1-c, BicPb1-c within the concentration and temperature ranges 0.1<or=c<or=1.0 and 400K<or=T<or=640K, respectively. Although the magnetic dipolar rate Rm exceeds the electric quadrupolar rate Re by almost an order of magnitude, both the separation of R into Rm and Re and of Re into its coherent part Re,coh and its incoherent part Re,inc could be carried out to approximately 10%. Details of the spectrometer (combination of a commercial pulse set up with an on line computer) and of the alloy preparation (capillary bunch samples) are given. The concentration and temperature dependence of both parts of Re can be described by the current theory of Re(c,T) for random substitutional metallic alloys.