Momentum conservation and the validity of the center-of-mass law are examined for systems made up of electrostatic charges and magnets, in terms of the requirements of special relativity theory. The approach used is that of a quasimicroscopic electromagnetic theory, in which the interaction of the field with material bodies is described by using models for these bodies which involve charge and current densities. It is shown that if small "electromagnetic mass" terms are neglected, both conservation of momentum and the center-of-mass law hold in all cases. In some cases a "hidden momentum" contained in stationary matter plays an important role, as pointed out recently by Shockley and James [W. Shockley and R. P. James, Phys. Rev. Lett. 18, 876 (1967).] In such cases the center-of-mass law can fail in nonrelativistic theory. This is illustrated by the discussion of a special model. Another case in which a "hidden momentum" required by relativity theory is important is the explanation of the null result of the Trouton-Noble experiment. This is discussed in Sec. V.