The investigation of the neuronal environment allows us to better understand the activity of a cerebral region as a whole. The recent experimental evidences of the presence of transporters for glutamate and GABA in both neuronal and astrocyte compartments raise the question of the functional importance of the astrocytes in the regulation of the neuronal activity. We propose a new computational model at the mesoscopic scale embedding the recent knowledge on the physiology of neuron and astrocyte coupled activities. The neural compartment is a neu-ral mass model with double excitatory feedback, and the glial compartment focus on the dynamics of glutamate and GABA concentrations. Using the proposed model, we first study the impact of a deficiency in the reuptake of GABA by astrocytes, which implies an increase in GABA concentration in the extracellular space. A decrease in the frequency of neural activity is observed and explained from the dynamics analysis. Second, we investigate the neuronal response to a deficiency in the reuptake of Glutamate by the astrocytes. In this case, we identify three behaviors : the neural activity may either be reduced, or enhanced or, alternatively, may experience a transient of high activity before stabilizing around a new activity regime with a frequency close to the nominal one. After translating theoretically the neuronal excitability modulation using the bifurcation structure of the neural mass model, we state the conditions on the glial feedback parameters corresponding to each behavior.