Abstract. The atmospheric carbon dioxide concentration plays a crucial role in the radiative balance and as such has a strong influence on the evolution of climate. Because of the numerous interactions between climate and the carbon cycle, it is necessary to include a model of the carbon cycle within a climate model to understand and simulate past and future changes of the carbon cycle. In particular, natural variations of atmospheric CO₂ have happened in the past, while anthropogenic carbon emissions are likely to continue in the future. To study changes of the carbon cycle and climate on timescales of a few hundred to a few thousand years, we have included a simple carbon cycle model into the iLOVECLIM Earth System Model. In this study, we describe the ocean and terrestrial biosphere carbon cycle models and their performance relative to observational data. We focus on the main carbon cycle variables including the carbon isotope ratios δ¹³C and the Δ¹⁴C. We show that the model results are in good agreement with modern observations both at the surface and in the deep ocean for the main variables, in particular phosphates, dissolved inorganic carbon and the carbon isotopes.