A theoretical study is made into the effect of the crystal, orbital, and charge structures on the magnetic structure and spin-wave spectra and on the antiferromagnetic resonance (AFMR) for R0.5Ca0.5MnO 3 crystals of monoclinic structure. The model assumes fixed crystal, charge, and orbital structures and enables one to determine the orbitally dependent exchange interaction and single-ion anisotropy for R = La, Pr, Tb. A 16-sub-lattice weakly noncollinear magnetic CE-structurc without a ferromagnetic component is obtained. The behavior of magnetic structure in an external magnetic field is simulated, and the values of fields of spin-flop-transition for different Rs are obtained. The law of spin-wave dispersion and the field dependence of the antiferromagnetic-resonance spectrum are calculated.