For equipment or plant replacement, when to replace an existing plant, fleet or a part of it, is one of the main concerns in decision-making. The thesis considers this decision-making problem using capital replacement models with a fixed planning horizon, and we took at the behaviour of optimal policy in this context. Application of the models is considered and we compare replacement models with a fixed planning horizon with replacement models with a variable planning horizon models comprising of two cycles. Capital replacement modelling in general and previous work done in the field are reviewed. The main work of this thesis is the study of the behaviour of optimal replacement policy for a single equipment/fleet over a fixed planning horizon, with a numerical investigation of the behaviour for non-like-with-like replacement. This is extended to describe the behaviour of optimal policy for replacement of a mixed fleet. A case study is presented that applies the fixed planning horizon model to a bus fleet; this fleet is operated by a Malaysian inter-city bus company. Finally we consider the challenger problem. Throughout, we recommend the use of a fixed planning horizon model rather than a two cycle variable-horizon model. The rent criterion is also our favoured criterion for decision-making; the rent criterion exists and is well behaved for all the models described. A dynamic programming approach is implemented for the like-with-like replacement problem over a fixed planning horizon for comparison with the economic life modelling approach of this thesis. We discuss the use of the different replacement decision models for supporting replacement decision-making in practical contexts.