A new approach to the modelling of chemical reactors and contactors is discussed, This approach argues that the dispersion should. under most circumstances, be based on Maxwell’s, rather than Fick’s diffusion law, As a pair of first-order partial differential equations of the hyperbolic type and requiring only inlet conditions, the wave model is more realistic physically, has a much wider range of validity and in many practical cases is simpler mathematically. Only mass transfer problems are considered, but the results apply equally well to the hydrodynamic dispersion of heat, It is explained why the standard dispersion model fails in many practical applications and why the new wave model gives much better results.