Abstract Optimization of tubular reactors in which the desired reaction is exothermic and reversible is considered. For the cases where there are no side reactions and there is no decay of catalyst various types of temperature control are investigated. The remaining cases considered are a) stable catalyst, irreversible decay of product and b) decaying catalyst, stable product. In each of these cases perfect indirect temperature control is treated. Particular attention is given to devising numerical methods which take advantage of the structure of the problem in question and to convenient representation of data.