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Abstract In this work we study linear and nonlinear cosmological interactions, which depend on dark matter and dark energy densities in the framework of general relativity. By using the Akaike information criterion (AIC) and the bayesian information criterion (BIC) with data from SnIa (Union 2.1 and binned JLA), $$\mathrm{H(z)}$$ H ( z ) , BAO and CMB we compare the interacting models among themselves and analyze whether more complex interacting models are favored by these criteria. In this context, we find some suitable interactions that alleviate the coincidence problem.