A kinetic model of growth and coalescence of oxygen and carbon precipitates has been proposed. This model in combination with the kinetic model of the formation of oxygen and carbon precipitates represents a unified model of precipitation in as-grown dislocation-free silicon single crystals during their cooling in the temperature range from 1683 to 300 K. It has been demonstrated that the results of the calculations are in good agreement with the experimental data obtained from investigations of grown-in microdefects.