Two searches for the production of Higgs bosons decaying into tau and mu leptons, using data collected with the DZero detector at the Fermilab Tevatron p-bar(p)collider, are presented. A search for the pair production of doubly charged Higgs bosons in the processq-bar(q) to H^{++}H^{--}, where H^{++} decays to tau-tau, mu-mu or tau-mu lepton pairs, with an integrated luminosity of up to L= 7.0 fb^{-1}, is presented. No significant excess of data over the expected SM background is observed and the results are used to set 95\% C.L. limits on the pair production cross section of doubly charged Higgs bosons in the range 90 < M_{H^{++}} < 200 GeV. A second search for the production of the Standard Model Higgs boson in the final state tau-tau-mu+X is presented, using an integrated luminosity of L=8.6 fb^{-1}. Again no significant excess of data is observed over the background expectation and 95% C.L. limits are set on the observed cross section relative to the Standard Model prediction, in the range 100 < M_{H} < 200 GeV.