We consider a dilute homogeneous suspension of rigid spherical particles with different size and density in a motionless Newtonian fluid, These particles are moving under gravity at low Reynolds and Stokes numbers(negligible fluid and particle inertia) and high Peclet numbers (negligible Brownian diffusion), Doublets are formed when two particles in relative motion are brought into contact by the action of the attractive van der Waals force. Trajectory calculations for particles with different densities indicate that as the reduced density ratio increases above unity, the percentage of particles captured on the front hemisphere decreases, and this generally results in smaller collision efficiencies. Furthermore, in contrast to the case of particles with equal density, a maximum of the collision efficiency occurs for a particle size ratio smaller than unity. Above a critical value of the reduced density ratio, the occurrence of a closed region of relative trajectories confines the capture sites mostly to the "rear" hemisphere of each particle. As the reduced density ratio increases above the critical value, this region grows larger and the collision efficiency may be estimated by a closed-form asymptotic solution.