This paper considers from a theoretical viewpoint the problem of the appearance of different magnetic structures in the series of compounds La1 − x Ca x MnO3, 0 ≤ x ≤ 1. It is assumed that the entire series possesses the structure of the GdFeO3 type. The problem is analyzed in the nearest-neighbor approximation with allowance for direct exchange, double exchange, and anisotropy energy (ten interaction parameters on the whole). The spin operator of double exchange interaction in the crystal between the different-valence ions of manganese Mn3+ and Mn4+ is the direct generalization of two-spin operator in the well-known problem of the Anderson-Hasegawa molecule. The minimization of the energy along the direction angles of magnetic sublattices leads to a set of transcendental equations, whose solutions give eleven types of magnetic configurations: two ferromagnetic, three collinear antiferromagnetic, and six noncollinear antiferromagnetic. As the concentration of calcium ions x changes, one spin configuration changes another as the ground state. The appearance of angular configurations in the system occurs only due to the simultaneous presence of direct Heisenberg interaction and substantially non-Heisenberg double exchange.