Mathematical models are presented which quantify the processes of evaporation and dissolution of components of crude oil in three situations: a spill on water, a spill on ice, and a spill under ice cover in which the oil lies between the water and ice phases. Constant spill area is assumed. The evaporation flux is calculated using a mass transfer coefficient based on windspeed and spill dimensions. The dissolution flux can be calculated from two models, a mass transfer coefficient approach and an eddy diffusivity approach involving the integration of a set of partial differential equations in depth and time. The selection of model parameters is discussed. For the three physical situations, using a synthetic crude oil, results are presented giving the relative rates of evaporation and dissolution and the aqueous phase concentration of selected hydrocarbons. The implications of the results for clean-up technology and aquatic toxicity are discussed, particularly with regard to spills under ice.