A novel sequential approach is proposed for the multiperiod synthesis of Heat Exchanger Networks (HEN) and Utility Systems of chemical processes and energy systems. The framework can be used also for single period problems. Given the set of hot and cold process streams with period dependent heat loads and target temperatures and a set of available utility systems, the algorithm determines the optimal utility system selection, design, and operation scheduling, as well as the optimal HEN. In this work, the approach of solving multiperiod problems by adopting (1) the Multiperiod Utility Integration and Scheduling model of Maréchal and Kalitventzeff, a modified formulation for (2) the Multiperiod Minimum Number of Units problem of Floudas and Grossmann, and (3) the Multiperiod Minimum Investment Network problem proposed by Floudas and Grossmann is improved by coupling the existing framework with the derivative-free hybrid algorithm PGS-COM of Martelli and Amaldi. Compared to the classic sequential approach,3 it is possible to select, design, and determine the optimal operation scheduling (switching on/off) of the utility systems, to design the HEN considering not only parallel configuration of utilities but also series of utility exchangers and hybrids configurations, to optimize the matches between streams looking for the minimum total cost rather than only for the minimum number of units, and to account for nonlinear cost functions not related to heat exchangers area. The proposed framework is tested on small-scale and medium-scale case studies in order to make a comparison with the classic sequential approach.