We explore the change in the period of axial rotation and in the radius of a magnetized compact star in a binary system, induced by the accretion on it of mass with angular momentum from the surface of its non-compact companion. No specific assumption is made concerning the accretion model, and the primary’s interior is described by the Fermi-Dirac statistics for degenerate matter. The rate of change with time of the period and radius is expressed in terms of the compact primary’s physical parameters and total absolute luminosity. The conditions are fully derived under which the above changes can be positive, negative or even vanish. In the case of the millisecond pulsars in binary X-ray sources the predicted values of the period time derivative, depending on the values of the accretion rate and. the absolute luminosity, can be positive or negative—if not vanishing—and they fall absolutely in the range 10−21 −10−17 ss−1, in good agreement with current observational data. The corresponding rate of change of radius, either positive or negative, fall in the range of 10−3 −10−1 cm y−1. Finally, it is proved that the well-known bursters can be explained by thermonuclear flash due to gravitational instability in the accreted matter, but their explanation as a result of direct contraction could be possible only for quite high accretion rates (>10−7 M ⊙ y−1). This last result indicates that, in contrast to the accretion-induced change in period, which can be of either sign irrespective of the primary’s age, the accretion-induced non-catastrophic contraction is impossible, while according to repent results the contraction in general is possible for young compact objects.