This paper addresses the problem of optimizing cyclic schedules of multiproduct continuous plants that consist of a sequence of stages each involving one production line that are interconnected by storage tanks. The problem involves a combinatorial part (sequencing of products) and a continuous part (duration of production runs and inventory levels). The problem is formulated as a large scale mixed-integer nonlinear program (MINLP) model that involves nondifferentiabilities in the inventory levels for the storage tanks. Binary variables and mixed-integer constraints are used to remove these nondifferentiabilities. A solution method based on variants of the generalized Benders decomposition and outer approximation is proposed for this scheduling problem. The method consists of an MINLP subproblem in which cycle times and inventory levels are optimized for a fixed sequence, and an MILP master problem that determines the optimal sequence of production. Examples are presented to compare the proposed decomposition method with the direct solution of the MINLP using an augmented penalty version of the outer-approximation method. The results show that the computational requirements can be greatly reduced in problems involving several hundred 0-1 variables, and several thousand continuous variables and constraints.