Heating of ions by two Alfvén waves propagating along an external magnetic field via nonresonant wave-particle interaction in low-b plasmas is studied using test-particle simulation. Due to subcyclotron ion resonance, the heating effect of the left-hand polarized Alfvén wave pair is 10% greater than that of the right-hand polarized pair. The results show that the perpendicular and parallel (to the external magnetic field) temperatures, as well as the parallel fluid velocity, vary sinusoidally with the phase difference. Furthermore, the magnitude of the oscillations decreases with the ratio of the frequencies of the two waves. When the frequency ratio reaches above 2, the effect of the phase difference vanishes. V C 2012 American Institute of Physics. [http://dx.