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We present high-resolution, high signal-to-noise spectra of the interstellar Na I and Ca II lines toward 7 stars in the direction of the Vela supernova remnant. We show that high velocity gas with a complex velocity structure exists toward these stars. The Ca II to Na I ratio generally increases as a function of velocity, but we find that there is a decrease of about 0.5 dex in the logarithmic ratio of these species near 100 km sec$^{-1}$. Several of the highest velocity components observed have unusually small values of N(Ca~II)/N(Na~I) compared to moderate velocity components and provide interesting counter-examples to the 'Routly-Spitzer' effect. These high velocity components probably trace sites of post-shocked gas in which pre-existing dust grains have not been destroyed. We have detected time variability in the absorption lines toward two stars, and in at least one case (the $\simeq$+190 km sec$^{-1}$ feature toward HD 72997) we also see systematic velocity shifts in the both the Na I and Ca II lines. These velocity shifts indicate that the gas is being accelerated at the rate of $\simeq$+1 km sec$^{-1}$ yr$^{-1}$. The high velocity gas distribution toward three stars in the sample separated by less than 6 arc minutes is consistent with an origin resulting from dynamical events other than the initial explosion that resulted in PSR 0833-045.
