Magnetization, electrical resistivity, and thermal expansion measurements have been performed on polycrystalline RTSb3 (R=La, Ce, Pr, Nd, Gd, Tb, and Dy; T=Cr, V) samples in order to study their magnetic properties. Depending on the rare-earth element, RTSb3 has been found to have either a purely ferromagnetic (or antiferromagnetic) phase or combination of antiferromagnetic (lower-temperature) and ferromagnetic (higher-temperature) phases. The antiferromagnetic order evolves from the ferromagnetic order as a result of the competition between R3+ and Cr3+ ions. As R is changed from La to Dy, the antiferromagnetic ordering of the R3+ ions becomes more prominent and predominate over the ferromagnetic ordering of Cr3+ for R=Gd, Tb, and Dy. Thermal expansion measurements show that the antiferromagnetic transition accompanies a drop in the sample dimension. The order of the ferromagnetic transition is found to be of the second order.