Laboratory searches for the detection of gravitational waves have focused on the detection of burst signals emitted during a supernova explosion, but have not resulted in any confirmed detections. An alternative approach has been to search for continuous wave (CW) gravitational radiation from the Crab pulsar. In this paper, we examine the possibility of detecting CW gravitational radiation from pulsars and show that nearby millisecond pulsars are generally much better candidates. We show that

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... e minimum strain h_c ~ 10E-26 that can be detected by tuning an antenna to the frequency of the milli- second pulsar PSR 1957+20, with presently available detector technology, is orders of magnitude better than what has been accomplished so far by observing the Crab pulsar, and within an order of magnitude of the maximum strain that may be produced by it. In addition, we point out that there is likely to be a population of rapidly rotating neutron stars (not necessarily radio pulsars) in the solar neighborhood whose spindown evolution is driven by gravitational radiation. We argue that the projected sensitivity of modern resonant detectors is sufficient to detect the subset of this population that lies within 0.1 kpc of the sun.