We report anharmonic vibrational spectra (fundamentals, first overtones) for the F-(H2O) and F-(H2O)(2) clusters computed at the MP2 and CCSD(T) levels of theory with basis sets of triple-zeta quality. Anharmonic corrections were estimated via the correlation-corrected vibrational self-consistent field (CC-VSCF) method. The CC-VSCF anharmonic spectra obtained on the potential energy surfaces evaluated at the CCSD(T) level of theory are the first ones reported at a correlated level beyond MP2. We have found that the average basis set effect (TZP vs aug-cc-pVTZ) is on the order of 30-40 cm(-1), whereas the effects of different levels of electron correlation [MP2 vs CCSD(T)] are smaller, 20-30 cm(-1). However, the basis set effect is much larger in the case of the H-bonded O-H stretch of the F-(H2O) cluster amounting to 100 cm(-1) for the fundamentals and 200 cm(-1) for the first overtones. Our calculations are in agreement with the limited available set of experimental data for the F-(H2O) and F-(H2O)(2) systems and provide additional information that can guide further experimental studies.