Mixed-effects models are commonly used in a large variety of disciplines to account for and describe the inter-individual variability of a population. A key question when adjusting a model to a population in this framework, is to understand and identify the parameters carrying the variability, i.e. those that can be considered constant in the population, referred to as `fixed-effects', and those that vary among individuals, referred to as `random effects'. This is particularly the case when the underlying model is a mechanistic model, for which parameters have a biological or physical meaning, for example. From a statistical point of view, this can be rephrased as a hypothesis testing problem, where one is interested in testing if the variances of a subset of the random effects are non-null. The issue of variance components testing in the context of linear mixed models has been addressed by several authors, and relates more generally to constrained statistical inference and hypothesis testing. We consider a testing procedure based on the likelihood ratio test statistics in the context of non linear mixed effects models. We establish theoretical results for the asymptotic distribution of the test statistics. Several special cases are detailed as well as general methods for a practical computation of the test.The methodology is applied to a nonlinear mixed model of plant growth, and tested on simulated and real data.