The hydrodynamic interactions between two fluid droplets freely suspended in an unbounded, immiscible fluid whose velocity at infinity is an arbitrary linear function of position are considered in the quasisteady situation. The droplets may differ in size and in viscosity. It is assumed that the interfacial tensions are sufficiently high so that the droplets retain a spherical shape. The effect of inertial forces on the motion of the fluids inside and outside the droplets is neglected. The relative velocity of the two droplet centers and the force dipole strengths of the two droplets, which are relevant in a calculation of the mean stress in a suspension of many such droplets subjected to bulk deformation, can be represented in terms of several scalar functions of relevant dimensionless parameters. These scalar functions are calculated for various values of the radii, viscosities, and separation distance of the droplets using a boundary collocation technique. The collocation results agree very well with the analytic and numerical results previously obtained for the cases of two solid spheres and two fluid spheres of identical viscosity.