Is the core mass-luminosity relation violated by the occurrence of the third dredge-up?

The core mass-luminosity (M-c - L) relation of thermally pulsing asymptotic giant branch (TP-AGB) stars is a key ingredient in synthetic calculations of their evolution. Recently, Herwig et al. (1998) have presented full calc ulations of TP-AGB models with strong dredge-up occurring already during ea rly thermal pulses. The resulting luminosity evolution differs appreciably from the simple linear M-c - L relation. In this paper, we show that at lea st part of the luminosity evolution can be understood as being the result o f two well-known effects: the gradual approach to the asymptotic behaviour that characterises the first thermal pulses, and the chemical, composition changes of the envelope. Both effects are already implemented in the M-c - L relations used in synthetic models. Consequently, these models are able t o reproduce the behaviour of full calculations. Whether additional effects, not yet taken into account, are present, can be decided only through addit ional calculations and data. We also comment on the validity of a linear M- c - L relation and its possible violation, as mentioned by Herwig et al.