The occurrence of chain-transfer introduces complications into calculations involving non-classical systems, both stationary and non-stationary. A procedure for treating the latter is described and applied in this paper. It resembles that formerly developed for systems without transfer and depends on setting up simultaneous differential equations for the time variation of , the mean radical size, and R , the total radical concentration. Changes in the overall reactivity of the group of radicals with changes in size-distribution are accommodated by a factor f ∫ , which plays a role similar to that of the factor f in the earlier treatment.The procedure is applied to the non-stationary phases arising when the rate of chain-initiation in a stationary reaction is abruptly increased or decreased. The time-variations of and R are calculated, together with the resulting pre- and after-effects (ΔM p r e ΔM a f t , respectively).Some new features in the time-variations mentioned have been found, notably the existence of reversal points (even in classical systems with transfer). The occurrence of transfer reduces ΔM p r e and ΔM a f t . Plots of log(ΔM p r e ) or log(ΔM a f t )) vs log(k p M) or log(k t o are very nearly - but not exactly - linear in the systems examined. Factors influencing the mean slopes of these lines are discussed.Semi-quantitative equations are developed relating ΔM p r e (or ΔM a f t ) to the reaction parameters. They may be used to estimate certain ratios of k p M and k t o from pre- (or after-) affects measured experimentally under prescribed conditions.