Detailed measurements are reported of the variation of spin-dependent resonance (SDR) signals at Si surfaces as a function of modulation frequency, light intensity, temperature and microwave power. These cannot be accounted for by the mechanisms assumed in current theories. A new model is proposed in which the resonant variation of the photoconductivity is explained in terms of two mechanisms, spin-dependent recombination and spin-dependent trapping, taking place at multivalent centres. An expression is obtained for the SDR signal, which for the first time is capable of explaining its observed magnitude. The model allows the calculation of the number of paramagnetic centres in different experimental conditions. Its validity is tested by comparison with experimental results and by the consistent results obtained in the calculation of capture coefficients in various experimental conditions.