The theory of the screening of scattering fields by the carrier space charge for a semiconductor heterolayer (in which the electrons are confined in one direction, with discrete quantum levels, and mobile in the perpendicular plane), is developed on a general basis. The layer geometry makes the screening depend on functions of the normal-direction wave functions and the perpendicular Fourier wave vector. Applications, in particular for Ga–Al–As heterostructures, are made to the scattering between the two-dimensional Bloch states due to phonons and due to ions. For the phonons, moderate effects of screening on the mobility, in practical conditions, are found. For optical-mode phonons the plasma resonance at the lattice frequency can appreciably modify the scattering. For the ions, strong screening and correspondingly enhanced mobility is possible, in particular for modulation doping; the result for the mobility in the latter case is applied to recent experimental data. The ’’secondary screening’’ effects due to the polarizability of the normal-direction quantum states are analyzed and are found to be normally small.