We study the four-body tau^+- -> nu_tau l^+- l^+- X^-+ decays where l=e or mu and X=pi, K, rho and K^* mesons. These decay processes violate the total lepton number (|Delta L|=2) and can be induced by the exchange of Majorana neutrinos. We consider an scenario where these decays are dominated by the exchange of only one heavy neutrino which produces an enhancement of the decay amplitude via the resonant mechanism. Searches for these novel decay channels with branching fractions sensitivities of (10^-7) can provide constraints on the parameter space of the Majorana neutrinos which are stronger than the ones obtained from Delta L=2 decays of charged pseudoscalar mesons.

REVTeX, 14 pages, 6 figures, four references added. Version accepted for publication in PRD