A statistical-mechanical description of the irreversible adsorption of interacting colloidal particles is developed. Our approach describes in a consistent way the interaction of particles from the bulk with adsorbed particles during the transport process towards the adsorbing surface. The macroscopic physical quantities corresponding to the actual process are expressed as averages over simpler auxiliary processes which proceed in the presence of a fixed number n of adsorbed particles. The adsorption rate verifies a generalized Langmuir equation, in which the kinetic resistance (the inverse of the kinetic coefficient) is expressed as the sum of a diffusional resistance and a resistance due to interaction with adsorbed particles during the transport process (blocking effect). Contrary to previous approaches, the blocking effect is not due to geometrical exclusion, instead it measures how the transport from the bulk is affected by the adsorbed particles. From the general expressions obtained, we have derived coverage expansions for the adsorption rate and the surface correlation function. The theory is applied to the case of colloidal particles interacting through DLVO potentials. This form of the kinetic coefficient is shown to be in agreement with recent experimental results, in which RSA fails.