Collision-rate theory is used to describe the collision and coagulation of aerosols moving in the free-molecule regime where the particle diameter σ(v) is small compared to the mean free path (g) of the suspending gas. A general expression is obtained for the rate of collision between particles. This relation accounts for the directing influences of electrical charging of the particles, external fields of force, and nonuniform states in the suspending medium, including surfaces of discontinuity. It is shown that the results of the free-molecule theory for thermal coagulation do not agree with the classical theory which has been corrected for the effects of large values of the ratio (g)/σ(ν). In addition, the free-molecule results indicate that the directing effects can substantially increase the coagulation rate, even for aerosol particles of small size.