Cells adherent on a cyclically stretched substrate with a periodically varying uniaxial strain are known to dynamically reorient nearly perpendicular to the strain direction. We investigate the dynamic reorientation of rat embryonic and human fibroblast cells over a range of stretching frequency from 0.0001 to 20 s(-1) and strain amplitude from 1% to 15%. We report quantitative measurements that show that the mean cell orientation changes exponentially with a frequency-dependent characteristic time from 1 to 5 h. At subconfluent cell densities, this characteristic time for reorientation shows two characteristic regimes as a function of frequency. For frequencies below 1 s(-1), the characteristic time decreases with a power law as the frequency increases. For frequencies above 1 s(-1), it saturates at a constant value. In addition, a minimum threshold frequency is found below that no significant cell reorientation occurs. Our results are consistent for the two different fibroblast types and indicate a saturation of molecular mechanisms of mechanotransduction or response machinery for subconfluent cells within the frequency regime under investigation. For confluent cell layers, we observe similar behaviors of reorientation under cyclic stretch but no saturation in the characteristic time with frequency, suggesting that cell-cell contacts can play an important role in the response machinery of cells under mechanical strain.