We analysed the Rossi X-ray Timing Explorer (RXTE) archival data of 1E 1048.1-5937 covering a time-span of more than one year. The spin-down rate of this source decreases by similar to 30 per cent during the observation. We could not resolve the X-ray flux variations because of contamination by eta Carinae. We find that the level of pulse frequency fluctuations of 1E 1048.1-5937 is consistent with typical noise levels of accretion-powered pulsars. Recent RXTE observations of 1E 2259+586 have shown a constant spin-down with a very low upper limit on timing noise. We used the RXTE archival X-ray observations of 1E 2259+586 to show that the intrinsic X-ray luminosity times-series is also stable, with an rms fractional variation of less than 15 per cent. The source could have been in a quiet phase of accretion with a constant X-ray luminosity and spin-down rate.