Accounting for spatial structures in econometric studies is becoming an issue of special interest, given the presence of spatial dependence and spatial heterogeneity problems arising in data. Generally, researchers have been employing parametric tests for detecting spatial dependence structures: Moran’s I and LM tests in spatial regressions are the most popular approaches employed in literature.However, this approach remains misleading in the presence of nonlinear spatial structures, inducing important biases in the estimation of the parameters of the model. In this paper we illustrate that issue by applying three non-parametrical proposals when testing for spatial structure in data. Empirical findings for the regions of the European Union show important failures of traditional parametric tests if nonlinearities characterise geo-referenced data. Our results clearly recommend employing new families of tests, beyond parametrical ones, when working in such environments.