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This article reports on recent searches for single-top-quark production by the CDF and DØ collaborations at the Tevatron. Neither two CDF analyses, using data corresponding to 695 pb-1 of integrated luminosity, nor a DØ search based on 370 pb-1 of data can establish a signal for this standard model process. These null results translate in upper limits on the cross section of 2.9 pb for the t-channel production mode and 3.2 pb for the s-channel mode at the 95% C.L. In addition, the DØ collaboration has searched for non-standard model production of single-top-quarks via a heavy W' boson. No signal of this process is found resulting in lower mass limits of 610 GeV/c2 for a left-handed W' and 630 GeV/c2 for a right-handed W' boson.