Fourier transform overtone spectra of SiHF3 were recorded in the region of 2500-9000 cm(-1) and vibrationally assigned. Experimental intensities were estimated. The 3 nu (1) overtone band at 6753 cm(-1) was observed to be more than 10 times weaker than the 4 nu (1) band. A reduced three-dimensional Hamiltonian model in terms of internal coordinates was employed to study the Si-H stretching and bending vibrations including 5 nu (1) and 6 nu (1) which were recently recorded using optoacoustic spectroscopy. Potential energy parameters were optimized by fitting to experimental band centers. The Fermi resonance between the Si-H stretching and bending motions was found to be insignificant. Band intensities were computed using ab initio one- and three-dimensional dipole moment surfaces (DMS) expanded to polynomials in terms of symmetrized internal coordinates. The intensity anomaly of 3 nu (1) is understood as resulting from cancellation of contributions by the linear and quadratic terms in the DMS expansion. The behavior of X-H stretching overtone intensities as excitation increases was also studied in the low and medium energy regions. Whether a rapid or a slow decrease of intensity occurs with increasing excitation depends strongly on the nonlinearity of the DMS. For some molecules, there is an almost complete cancellation of contributions from the lower order terms in the DMS so that the accuracy of the computed overtone intensities is mainly limited by the uncertainty of the higher order expansion coefficients in the DMS.