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We present a search for supersymmetry in the R-parity violating resonant production and decay of smuons and muon sneutrinos in the channels μ̃→ χ̃10μ, μ̃→ χ̃2,3,40μ, and ν̃μ→ χ̃1,2±μ. We analyzed 0:38 fb-1 of integrated luminosity collected between April 2002 and August 2004 with the D0 detector at the Fermilab Tevatron Collider. The observed number of events is in agreement with the standard model expectation, and we calculate 95% C.L. limits on the slepton production cross section times branching fraction to gaugino plus muon, as a function of slepton and gaugino masses. In the framework of minimal supergravity, we set limits on the coupling parameter λ ′211, extending significantly previous results obtained in Run I of the Tevatron and at the CERN LEP collider.