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We present radio and optical observations of the pulsar/B-star binary, PSR~J0045$-$7319, the only known pulsar in the Small Magellanic Cloud. Radio timing observations of the pulsar reveal low-level systematic residuals after a fit for a simple spin-down model using a standard Keplerian orbit. We discuss various possible origins of the residuals. We also present results of optical spectroscopic observations of the companion B-star. The detection of Doppler shifts of the companion's absorption lines would make the PSR~J0045$-$7319 system the first effective double-lined spectroscopic binary containing a radio pulsar, and allow the determination of the mass ratio of the components.
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