In this paper the modelling objective is to determine the drug alternation time which minimises the formation of resistant tumour cells when delivering two non-cross resistant chemotherapeutics given such drugs cannot be delivered simultaneously and constraints due to pharmacokinetics and protocol rest phases. We initially consider cell cycle phase non-specific models, as investigated by Goldie and Coldman. By extending previous work, these models are generalised to consider chemotherapeutic S-phase specificity. We find with the cell cycle phase non-specific models that once the alternation time of the drugs is reduced below a critical threshold, a substantial improvement in protocol outcome is predicted. Extensive improvements are also observed for the S-phase specific investigation if the drugs can be alternated extremely rapidly. However, this is typically impossible due to pharmacokinetic constraints. Under such Circumstances, the most appropriate choice of the alternation time can depend sensitively on the median and variance of the tumour cell cycle time in a complicated manner. For schedulings motivated by Capecitabine protocols, we find that switching the drugs only once, or at most twice, between rest phases gives the most reliable alternation time. The main and novel conclusion of this paper is the modelling prediction that one must be much more specific in the choice of the protocol alternation time if attempting to observe the improvements promised by Goldie and Coldman's alternation hypothesis for the rest phases, pharmacokinetics and delivery mechanisms typically encountered in cell cycle phase specific chemotherapy protocols. (c) 2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.