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We investigated the long-term spin properties of the anomalous X-ray pulsar(AXP) 1E 1841-045 by performing a temporal analysis of archival RXTEobservations spanning about 5.2 yr from 2006 September to 2011 December. Weidentified two peculiar timing anomalies within ~1 yr of each other: a glitchwith Delta(nu)/nu ~ 4.8 x 10^{-6} near MJD 54303; and an anti-glitch withDelta(nu)/nu ~ -5.8 x 10^{-7} near MJD 54656. The glitch that we identified,which is the fourth glitch seen in this source in the 13 yr of RXTE monitoring,is similar to the last two detected glitches. The anti-glitch from 1E 1841-045,however, is the first to be identified. The amplitude of the anti-glitch wascomparable with that recently observed in AXP 1E 2259+586. We found nosignificant variations in the pulsed X-ray output of the source during eitherthe glitch or the anti-glitch. We discuss our results in relation to thestandard pulsar glitch mechanisms for the glitch, and to plausiblemagnetospheric scenarios for the anti-glitch.

A glitch and an anti-glitch in the anomalous X-ray pulsar 1E 1841-045