In an auditory lexical decision task experiment, the performances of highly proficient early Spanish- Catalan and Catalan-Spanish bilinguals were contrasted using Catalan materials (Sebastian-Galles et al. 2005, JML). In this task, two types of experimental non-words were specifically constructed by substituting the Catalan phoneme /E/ for a Catalan /e/, or vice versa. As expected from previous research, Spanish-Catalan bilinguals showed great difficulties in discriminating experimental words from non-words. Indeed, these mistakes were manifestations of a perceptual assimilation in the context of lexical decision; both Catalan phonemes being 'mapped' to a Spanish /E/. Especially interesting was the asymmetry across both experimental conditions for Catalan-dominant bilinguals. They made more mistakes for /E/->/e/ changes, than for /e/->/E/ ones. This pattern was taken as evidence of a developed acceptance for mispronounced Catalan /E/-words, i.e. a sort of long term plasticity, the origin of this phenomenon being exposure to a bilingual environment, where such mispronunciations by Spanish-dominant bilinguals abound. These results lend themselves well to biophysically realistic neurodynamical modelling employing descriptions at the level of spiking neurons and the synaptic activity which evokes the spikes in the neuron membrane potential. Using such a model, we construct a network of pools of neurons, which consequently engage in competitive and cooperative interactions with each other, trying to represent their input in a context-dependent way. Thus we can carefully study the underlying nonlinear dynamics of the context-dependent assimilation effect as manifested in the behavioural results, by using mean-field techniques as well as by running full spiking simulations, looking for stable areas in parameter space exhibiting such phenomena. In particular, the asymmetry phenomenon observed for Catalan-dominant bilinguals, i.e. the 'environmental assimilation effect', is shown by varying network connection strengths, thus representing effects of long-term plasticity. This model makes specific predictions about the consequences at the phoneme level of different patterns of asymmetries (at the lexical-contextual level). Additional data comparing the (behavioural) performance of Catalan-Spanish bilinguals in a discrimination task and a lexical decision task will be presented. The use of a biophysically realistic model further gives us possibilities of making predictions at all neuroscientific levels, namely microscopic (single cells), mesoscopic (ERPs, fMRI) and macroscopic (behaviour), thereby opening for an extension of our study to other types of data when further results are obtained in planned and current relevant experiments.