The osmophoretic motion of two spherical vesicles in a constant gradient of solute concentration is analyzed using a method of reflections. The vesicles are oriented arbitrarily with respect to the gradient, and they are allowed to have different semipermeable membranes, hold arbitrary solutes, and possess unequal sizes. The method of reflections is based on an analysis of the solute concentration and fluid velocity disturbances produced by a single spherical vesicle placed in an arbitrarily varying concentration field. The quasisteady results for two-vesicle interactions are correct to O(r(12)(-7)), where r(12) is the distance between the vesicle centers. Our analytical results are found to be in good agreement with the numerical solution obtained using spherical bipolar coordinates. Based on a microscopic model the results for two-vesicle interactions are used to determine the effect of the volume fraction of vesicles of each type on the average osmophoretic velocity in a bounded suspension. For a suspension of identical vesicles, this average velocity is increased as the vesicle volume fraction is increased.