A study of the dyeing behaviour of modified polyester fibre in the presence of cationic dyes has been carried out. The initial and final dyeing temperatures and the rate of heating of the dyebath for different initial concentrations of dye have been calculated from the results of isothermal dyeings at different temperatures and the Arrhenius equation. The equivalent concentrations of the dyes tested, i.e. concentrations producing the same exhaustion curve, have been determined. The initial and final temperatures of the process for any given rate of dyeing have been calculated.