This paper presents the first ab initio attempt to construct the stretching fundamentals nu-FX and nu-F...N (X = H, D, Li) in the FX...NH3 complexes taking into account the mechanical anharmonicity. A potential-energy surface V(r(FX),R(F...N)) grid was generated at the self-consistent-field and second-order Moller-Plesset levels. The coefficients fitting the potential-energy surface up to the fourth order have been used to compute the nu-FX and nu-F...N stretching modes. The vibrational problem is solved by means of a variational treatment which includes the effects of mechanical anharmonicity. The results are compared with the available experimental data.