Abstract We introduce two new functions, known as the q( T) and Q( T) functions, which describe how close a system is to quasi-equilibrium during the production of thermally stimulated conductivity (TSC) and thermoluminescence (TL). These functions are related to physically meaningful quantities (i.e. the various rates of recombination, excitation and retrapping) and are closely related to the kinetic-order function, P( T). From from a numerical analysis of the rate equations describing the flow of charge carriers between various energy levels in a simple model for TL and TSC we demonstrate that usual equation for describing TL emission is related to the actual TL peak by the Q( T) function, for first-order kinetics. The use of the simplified function to analyze TL and TSC data leads to errors which can be directly traced to the departure of the system from quasi-equilibrium. We show how the q( T) function can be obtained experimentally and we present arguments to demonstrate that first-order kinetics are likely to be the most common in nature.