Experimental and theoretical evidence for the existence of mobile, transitory precursor states and for the importance of lateral interactions between chemisorbed species is briefly surveyed. Generalised rate expressions for adsorption and desorption are derived which specifically take into account the existence of intrinsic and extrinsic precursor states, and which can be readily adapted to account for dissociative or non-dissociative adsorption, with and without interactions, and which also account for the possibility of direct transfer to or from the chemisorbed state, without trapping in the intrinsic precursor state. These expressions, derived using kinetic schemes, are shown to be identical with rate expressions obtained from a successive site statistical model. Thermodynamic conditions are used to restrict the number of parameters in these expressions.