The evolution of a cometary nucleus depends on the size distribution of the dust content. If all the dust particles are small enough, they will all be thrown off into the coma; the secular decrease in the comet's brightness is due simply to the decrease in the nuclear radius, and the comet eventually disintegrates. On the other hand, if larger grains are present, they will start to form spots of a low-emissivity mineral envelope on the surface of the nucleus; in this case, the decrease in brightness is due to the increase in the area of the screened part of the surface, and the reduction in the nuclear radius is comparatively small. It is shown that after about 90% of the surface has been screened, the rate of screening increases considerably, as smaller particles become trapped between the larger ones; and there will be a corresponding acceleration in the brightness decrease. These nuclei are eventually covered with a solid mineral envelope, and they are transformed into asteroids.