In the present paper, a kinetic model of the transition region between the collision-dominated and the collisionless domains of the neutral planetary atmospheres is presented. The Boltzmann equation is solved to study the escape of hydrogen and helium from the terrestrial atmosphere through a background of oxygen. The escape of hydrogen atoms from the atmosphere of Mars is also considered. A spectral method, initially developed to study the polar wind, is used to solve the collisional Boltzmann equation. The effects of the planetary curvature and the gravitational force are taken into account. The escape flux is found to be reduced by a factor 0.9 for helium and 0.6 for hydrogen escaping from the terrestrial atmosphere compared with purely exospheric Jeans' flux. For hydrogen escaping from Mars, the factor is around 0.57. Density and temperature profiles are also provided. The results are compared with those of previous collisional models based on Monte Carlo simulations or on the Boltzmann equation with different assumptions.