In order to clarify the mechanism of exchange interactions in orthomanganites with perovskite structure a magnetic study of parent compounds as a function of stoichiometry has been made. It was shown that the LaMnO2.99 is a weak ferromagnet with TN=147 K while LaMnO3.13 and La0.9MnO3.05 are ferromagnets with TC=160 and 240 K, respectively. The magnetic data indicate that the mixed magnetic state involving ferro- and antiferromagnetic domains is realized in the intermediate range of oxygen content. The RMnO3+y (R=Nd, Sm, Eu, Gd) are inhomogeneous antiferromagnets. The temperatures of start of magnetic moments freezing inside ferromagnetic clusters depend slightly on stoichiometry and for y∼0 are equal 83, 65, 47, and 22 K, respectively. The coercive field for LaMnO3 is 6 kOe at 4.2 K while that for EuMnO3 is much higher—26 kOe. It is worth noting that the Neel temperatures of RMnO3 (R=Eu, Gd, Tb, Dy) are estimated to be about 40 K independently of the type of rare-earth ion. Magnetic moments of Gd, Tb, and Dy in the rare-earth sublattice are antiferromagnetically ordered below 6–7 K. Applying external fields induces the antiferromagnet–ferromagnet transition in rare-earth sublattice. Hcr at 2 K for RMnO3 (R=Gd, Tb, Dy) are measured to be about 5, 12, and 10 kOe, respectively. In contrast to rare-earth compounds, the BiMnO3 is ferromagnet below 98 K. The deviation from stoichiometry as well as replacement of Bi ions by Sr, Ca, or La ions leads to the suppression of the long-range ferromagnetic order. Magnetic properties are discussed in terms of super exchange interactions between manganese ions via oxygen taking into account the 3d-orbital ordering that occurs in LaMnO3 and TbMnO3 at 400 and 1200°C, respectively.