This paper deals with a number of ideas which may be applicable when investigating the use of modern optimal control theory to certain cancer chemotherapy problems. A new mathematical model is developed and incorporates the growth kinetics of the tumour together with a cell loss term involving the therapeutic agent. Then several new models with different performance criteria are discussed for populations of normal and tumour cells. The final section deals with a new control problem for a model having two compartments and a cell-cycle-specific chemotherapeutic agent.