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Variation in the angle $\alpha$ between a pulsar's rotational and magneticaxes would change the torque and spin-down rate. We show that sudden increasesin $\alpha$, coincident with glitches, could be responsible for the persistentincreases in spin-down rate that follow glitches in the Crab pulsar. Moreover,changes in $\alpha$ at a rate similar to that inferred for the Crab pulsaraccount naturally for the very low braking index of the Vela pulsar. If$\alpha$ increases with time, all pulsar ages obtained from the conventionalbraking model are underestimates. Decoupling of the neutron star liquidinterior from the external torque cannot account for Vela's low braking index.Variations in the Crab's pulse profile due to changes in $\alpha$ might bemeasurable.Comment: 14 pages and one figure, Latex, uses aasms4.sty. Accepted to ApJ  Letter

Are We Seeing Magnetic Axis Reorientation in the Crab and Vela Pulsars?