A mathematical model of orientation selectivity in a single hypercolumn of the primary visual cortex developed in a previous work [Ursino, M., & La Cara, G.-E. (2004). Comparison of different models of orientation selectivity based on distinct intracortical inhibition rules. Vision Research, 44, 1641-1658] was used to analyze the possible mechanisms underlying tilt aftereffect (TAE). Two alternative models are considered, based on a different arrangement of intracortical inhibition (an anti-phase model in which inhibition is in phase opposition with excitation, and an in-phase model in which inhibition has the same phase arrangement as excitation but wider orientation selectivity). Different combinations of parameter changes were tested to explain TAE: a threshold increase in excitatory and inhibitory cortical neurons (fatigue), a decrease in intracortical excitation, an increase or a decrease in intracortical inhibition, a decrease in thalamo-cortical synapses. All synaptic changes were calculated on the basis of Hebbian (or anti-Hebbian) rules. Results demonstrated that the in-phase model accounts for several literature results with different combinations of parameter changes requiring: (i) a depressive mechanism to neurons with preferred orientation close to the adaptation orientation (fatigue of excitatory cortical neurons, and/or depression of thalamo-cortical synapses directed to excitatory neurons, and/or depression of intracortical excitatory synapses); (ii) a facilitatory mechanism to neurons with preferred orientation far from the adaptation orientation (fatigue of inhibitory cortical neurons, and/or depression of thalamo-cortical synapses directed to inhibitory neurons, and/or depression of intracortical inhibitory synapses). By contrast, the anti-phase model appeared less suitable to explain experimental data.