The traditional approach for modelling the particle-size distributions (PSDs) in crystallisers gives rise to partial differential equations. These equations are associated with ideal forms of the residence-time distribution (RTD), and cannot be generalised to incorporate arbitrary RTDs. In the present work, an alternative approach is described, and new, integral equations are derived. These incorporate arbitrary RTDs and a very general model of growth. The general, integral equations are simplified for more specific cases; these simple equations often have intuitive justifications. They also suggest new solution strategies for simulating PSDs in practice. The two approaches, differential and integral, are compared. The integral approach can handle dynamic responses, including discontinuities, with ease. An industrial case study, simulating the start-up of two crystallisers in series, is presented in detail. The rapid start-up causes abrupt variations in the PSDs, and the integral approach gives a much more accurate and efficient solution in this case.