It is shown that if the phase difference between oscillating electric and magnetic fields is judiciously chosen, particles are accelerated along a line that is perpendicular to those fields. Moreover, the direction of acceleration depends on the particle mass, so that species of (even small) mass difference are accelerated in opposite directions. Two configuraions are addressed. One configuration is of linearly-polarized electric and magnetic fields. In a second configuration, a steady axial magnetic field is added to circularly polarized oscillating fields. For an appropriate phase difference, charged particles, the cyclotron frequencies of which lie on the two opposite sides of the cyloton resonance, are accelerated in opposite directions. This phase-induced mass-selective acceleraion can be the basis for a novel mass separation scheme.