The compression of two-dimensional colloidal monolayers consisting of polystyrene particles at an oil-water interface is investigated theoretically. Expressions for the pair-particle interactions are derived both for point particles and for particles of radius R. The resulting expressions for the interaction energies are employed in a molecular dynamics simulation of the surface pressure of these monolayers. A comparison of the theoretical results with recent observations allows the determination of the dominant interaction mechanisms in the experimental system. Possible physical interpretations of the interaction mechanisms between the particles are discussed.