We present a detailed study of RNi1-xBi2+-y (R = La-Nd, Sm, Gd-Dy) single
crystals by measurements of stoichiometry and temperature dependent magnetic
susceptibility, magnetization, and electrical resistivity. This series forms
with partial Ni occupancy as well as a variable Bi occupancy. For R = Ce-Nd,
Sm, Gd-Dy, the RNi1-xBi2+-y compounds show local-moment like behavior and order
antiferromagnetically at low temperatures. Determination of anisotropies as
well as antiferromagnetic ordering temperatures for RNi1-xBi2+-y (R = Ce-Nd,
Sm, Gd-Dy) have been made. Although crystalline samples from this family
exhibit minority, second phase superconductivity at low temperatures associated
with Ni-Bi and Bi contamination, no evidence of bulk superconductivity has been
observed