The RNiSb compounds (R=Ho, Er, Tm, Yb and Y) and some selected solid solution members such as (Zr1-xErx)Ni(Sn1-xSbx) and ErNiSb1-xPnx (Pn=As, Sb, Bi) have been studied. They all crystallize in the MgAgAs structure type, which can be considered as a NaCI structure type in which half of the interstitial tetrahedral sites are occupied by Ni atoms. The measured values of the Seebeck coefficients, at room temperature, are positive for RNiSb (R=Ho, Er, Yb and Y) compounds and ErNiSb1-xPnx (Pn=As, Sb, Bi) solid solutions, but for (Zr1-xErx)Ni(Sn1-xSbx) members vary from negative to positive values when 0 < x < 1. Some of these compounds show metallic conductivity while others exhibit thermally activated charge transport. Solid solutions of these materials have lower thermal conductivities than the pure members, RNiSb (R=Ho, Er, Yb and Y) and ZrNiSn. The electronic structures of RNiSb compounds, where R is Y, La, Lu, and Yb, have been studied with density functional theory. The results of the calculations for these systems, except for the Yb compound, indicate narrow gap semiconductors with large effective masses near the conduction band extrema. The Yb system is expected to show heavy fermion characteristics.