We report the crystal growth and structural, magnetic, conductivity, and specific heat investigations of Rb_1-xFe_2-ySe₂ single crystals with varying stoichiometry prepared by self-flux and Bridgman methods. The system exhibits a strongly anisotropic antiferromagnetic behavior below 400 K. Bulk superconductivity is found in samples with Fe concentrations 1.53<2-y<1.6, whereas for 2-y[removed]1.6, insulating and semiconducting behavior is observed, respectively. Within the measured range of variation of the Rb concentration (0.6-0.8) no correlation between the Rb content and the lattice parameters of the samples was found. The superconducting samples show the smallest value of the lattice parameter c compared to the nonsuperconducting samples. The sharpest transition to the superconducting state, the highest transition temperature T_c of 32.4 K, and the highest diamagnetic response corresponding to a critical current density j _c of 1.6×104 A/cm2 (at 2 K) is found for compositions close to Rb₂Fe₄Se₅. Upper critical fields H_c2 of ∼250 kOe for the in-plane and 630 kOe for the interplane configurations are estimated from resistivity studies in magnetic fields. In the nonsuperconducting samples with the Fe concentration below 1.45, both specific heat and susceptibility revealed an anomaly at 220 K, which is not related to antiferromagnetic or structural transformations. Comparison with the magnetic behavior of nonsuperconducting samples provides evidence for the coexistence of superconductivity and static antiferromagnetic order.