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Magnetically actuated swimming of microscopic objects has been attracting attention partly due to its promising applications in the bio-medical field and partly due to interesting physics of swimming in general. While colloidal particles that are free to move in fluid can be an attractive swimming system due it its simplicity and ability to assemble in situ, stability of their dynamics and the possibility of stable swimming behavior in periodically varying magnetic fields has not been considered. Dynamic behavior of two magnetically interacting colloidal particles subjected to rotating magnetic field of switching frequency is analyzed here and is shown to result in stable swimming without any stabilizing feedback. A new mechanism of swimming that relies only on rotations of the particles themselves and of the particle pair axis is found to dominate the swimming dynamics of the colloidal particle pair. Simulation results and analytical arguments demonstrate that this swimming strategy compares favorably to dragging the particles with an external magnetic force when colloidal particle sizes are reduced. [ABSTRACT FROM AUTHOR]