Marine ecosystem models are an important tool to assess the role of the ocean biota in climate change and to identify relevant biogeochemical processes by validating the model outputs against observational data. For the assessment of the marine ecosystem models, the existence and uniqueness of an annual periodic solution (i.e., a steady annual cycle) is desirable. To analyze the uniqueness of a steady annual cycle, we performed a larger number of simulations starting from different initial concentrations for a hierarchy of biogeochemical models with an increasing complexity. The numerical results suggested that the simulations finished always with the same steady annual cycle regardless of the initial concentration. Due to numerical instabilities, some inadmissible approximations of the steady annual cycle, however, occurred in some cases for the three most complex biogeochemical models. Our numerical results indicate a unique steady annual cycle for practical applications.