The purpose of this paper is to model numerically the dynamics of CO2 and 222Rn in cave atmospheres, particularly in the noteworthy Cave of Altamira (Spain). We aim to get a better understanding of the nature of these dynamics and their couplings with climatic controls, more specifically the soil water content, which role in the said dynamics poses some questions. For the first time, we apply the global modeling technique in the field of cave microclimate and atmospheric composition. The global modeling technique is a methodology based on the theory of nonlinear systems and designed to extract mathematical models directly from observational time series. We were able to extract four global models from our data. These models represent a step forward from the existent conceptual ones. They also show that CO2 and 222Rn dynamics can be approximated by low-dimensional, deterministic systems, which can be chaotic or, at least, close to chaos; this has decisive methodological consequences for future research. Moreover, the global modeling technique was used for the first time in a non-autonomous formulation; this enabled the possibility of studying the influence of the external forcing (soil water content) on the gas concentration in different scenarios.