Nuclear hybrid energy systems (NHESs) have been proposed as an effective element to incorporate high penetration of clean energy (e.g., nuclear and renewable). This paper focuses on the operations optimization of two specific NHES configurations to address the variability raised from wholesale electricity markets and renewable generation. Both analytical and numerical approaches are used to obtain the optimal operations schedule. Key economic figures of merit are evaluated under optimized and constant (i.e., time-invariant) operations to demonstrate the benefit of the optimization, which also suggests the economic viability of the considered NHESs under the proposed operations optimizer. Furthermore, sensitivity analysis on commodity prices is conducted for better understanding of the considered NHESs.