We present the results of a GHRS program to monitor the absorption lines in the spectrum of the Seyfert 1 galaxy NGC 4151 caused by outflowing gas from the nucleus. Although we see subtle changes over the four year period in the GHRS spectra of the broader of the absorption features, the wavelength constancy of all the features is remarkable. The limits on the secular acceleration suggest that either (1) The absorbing clouds are well beyond the broad emission line region, or (2) The clouds are experiencing significant drag from an intercloud medium. The exception to this constancy occurred during one of the epochs of our monitoring when a broad shallow C IV trough appeared at an outflow velocity of 3750 km/s and then subsequently disappeared.