This paper proposes a linear disjunctive model to solve a multistage transmission expansion planning problem (MTEP) considering N - 1 security constraints. The use of a disjunctive linear model guarantees finding the optimum solution of the problems using existing classical optimization methods. For large-scale systems, when finding the optimum or even high-quality solutions of the MTEP problem is not possible in polynomial time, a search space reduction methodology (SSRM) is proposed. By using SSRM, it is possible to obtain very high-quality solutions or in most cases the optimum solution of the MTEP problem. The N - 1 security constraint indicates that the transmission system must be expanded in such a way that, despite the outage of a system line (a pre-defined set of contingencies), the system continues to operate properly. The model was implemented using a modelling language for mathematical programming (AMPL) and solved using the CPLEX, which is a commercial solver. The IEEE 24-bus, Colombian 93-bus, and Bolivian 57-bus systems are used to evaluate and show the performance of the proposed mathematical model and the search space reduction strategy.