Mode-I fracture behavior of fully-lamellar polycrystalline gamma-TiAl + alpha(2)-Ti3Al intermetallic alloys and the role of Ti-V base beta-phase precipitates of different thermodynamic stability have been studied using a finite element method. A rate-dependent, finite-strain, crystal-plasticity based materials constitutive model is used to represent the deformation behavior of both the gamma-TiAl + alpha(2)-Ti3Al lamellar matrix and the beta-phase precipitates. Within the matrix colonies, fracture is assumed to take place throughout the alpha(2)-Ti3Al lamellae. In addition, fracture along colony boundaries and matrix/precipitate interfaces is considered. The constitutive behavior of all fracture interfaces is modeled using a cohesive-zone formulation. The analysis is carried out using the commercial finite element program Abaqus/Standard within which the material state is integrated using an Euler-backward implicit formulation. The results obtained show that the main mechanism of crack growth is nucleation of secondary cracks along alpha(2)-Ti3Al lamellae ahead of the main crack and their subsequent link-up with the tip of the main crack. The resulting fracture resistance curve acquires the characteristic step-wise shape. Both stable and metastable beta-phase precipitates are found to have a beneficial effect on the fracture resistance of the material. However, the effect is not very significant and metastable beta-phase precipitates appear to be a little bit more beneficial. All these findings are consistent with their experimental counterparts.