There are many known complex systems with a relaxation oscillation behavior, characterized by a periodic phenomenon where relatively stable periods are interrupted abruptly by a sharp transition when a critical point is reached, shifting to a contrasting state. Some examples of these complex systems are Van der Pol Oscillator, Lotka-Volterra equations, both showing this stable to unstable shifting, or even glacial - interglacial changes in the Earth System, which may also obey to the dynamics of a relaxation oscillator rather than to a critical bifurcation. For this work, an exhaustive analysis of Van der Pol and Lotka-Volterra oscillators has been carried out to nd a statistic methodology that allow us to predict the critical point at which the shifting between stable and unstable states will be produced, with the aim of apply that methodology to the glacial-interglacial oscillations of the climate system. First of all, oscillator's atractor has been analyzed to study the stability of the system in front of noise, giving us an idea of how stable is the system to small perturbations. Then, several statistic descriptors have been analyzed such as autocorrelation at lag 1, variance or autoregression, used to show if there is any characteristic slowing down of the uctuations previous to unstable shift. The resulting methodology has been applied to a model of glacial-interglacial oscillations (García-Olivares and Herrero 2013, Clim. Dyn) to analyze the relaxation oscillations of CO2 and global ice volume time series

IV Congress of Marine Sciences, 11-13 June 2014, Las Palmas de Gran Canaria.-- 1 page

Peer Reviewed