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We describe a search for the pair production of first-generation scalar and vector leptoquarks in the ee j j and eν jj channels by the DO. Collaboration. The data are from the 1992–1996 pp̅ run at √s =1.8 TeV at the Fermilab Tevatron collider. We find no evidence for leptoquark production; in addition, no kinematically interesting events are observed using relaxed selection criteria. The results from the ee j j and eν jj channels are combined with those from a previous DO. analysis of the νν jj channel to obtain 95% confidence level (C.L.) upper limits on the leptoquark pair-production cross section as a function of mass and of β, the branching fraction to a charged lepton. These limits are compared to next-to-leading-order theory to set 95% C.L. lower limits on the mass of a first-generation scalar leptoquark of 225, 204, and 79 GeV/c2 for β =1, ½, and 0, respectively. For vector leptoquarks with gauge (Yang-Mills) couplings, 95% C.L. lower limits of 345, 337, and 206 GeV/c2 are set on the mass for β =1, ½, and 0, respectively. Mass limits for vector leptoquarks are also set for anomalous vector couplings.