Identifying modal analysis as the Galerkin (projection) method, the paper provides general conditions for applying the modal technique to the optimal control system synthesis of a nuclear reactor. It is shown that under some very general restrictions on the performance index the Galerkin method is applicable to the Hamilton-Jacobi canonical equations whenever they are applicable to the equations describing the mathematical model of a reactor. Using the Keldish theory of operator families, the conditions for completeness of the eigenvectors of the Hamilton-Jacobi operator are established. If these vectors are used as expanding functions in the Galerkin method a rather simple algorithm for computing the optimal control law can be obtained. The paper also provides an iterative variational method for the solution of an eigenvalue problem, which enables on-line implementation of the overall optimization algorithm through a two-level control system. Reactor models for a power control system and a flux distribution control system synthesis ore particularly investigated. The methods are illustrated in a simple example of a slab reactor.