In this paper we show that pseudomorphically strained heterostructures of InAsxP1-x/InP may be an alternative to lattice-matched heterostructures of In1-xGaxAsyP1-y/InP for optoelectronic applications. We first studied the group-V composition control in the gas-source molecular beam epitaxy (GSMBE) of the GaAs1-xPx/GaAs system. Then we studied GSMBE of strained InAsxP1-x/InP multiple quantum wells with the ternary well layer in the composition range 0.15 < x < 0.75. Structural and optical properties were characterized by high-resolution x-ray rocking curves, transmission electron microscopy, absorption and low-temperature photoluminescence measurements. High-quality multiple-quantum-well structures were obtained even for highly strained (up to 2.5%) samples. The achievement of sharp excitonic absorptions at 1.06, 1.3 and 1.55-mu-m at room temperature from InAsxP1-x/InP quantum wells suggests the possibility of long-wavelength optoelectronic applications.