This paper presents two types of two-phase AC/AC matrix converter structures based on two-leg and three-leg configurations, along with modulation strategies, and their realization for two-phase drive systems. The converter topologies directly link three-phase input AC lines to two-phase output AC loads through switching devices with no intermediate DC conversion and concomitant DC-link elements. Two individual modulation techniques for the two-leg and the three-leg based structures, based on space vector algorithm, are developed to synthesize sinusoidal output waveforms with variable amplitude and variable frequency from input AC voltages. The proposed control schemes allow independent magnitude controllability and quadrature phase angle for two output phases. Thus, the converter topologies and their modulation schemes make the two-phase matrix converter commensurate with both balanced and unbalanced two-phase loads. Simulation and experimental results confirm the feasibility of the structures and the control methods for the converters.