Here we analyze the relation between the search for muonium to antimuonium conversion and the 3-3-1 model with doubly charged bileptons. We show that the constraint on the mass of the vector bilepton obtained by experimental data can be evaded even in the minimal version of the model since there are other contributions to that conversion. We also discuss the condition for which the experimental data constraint is valid.PACS number͑s͒: 11.30. Fs, 11.30.Hv, 12.60.Ϫi, 36.10.Dr Recently a new upper limit for the spontaneous transition of muonium (M ϵ ϩ e Ϫ ) to antimuonium (M ϵ Ϫ e ϩ ) has been obtained ͓1͔. This implies constraints upon the models that induce the M →M transition. One of them is the 3-3-1 model proposed some years ago ͓2͔. Here we would like to discuss the conditions in which this constraint can be evaded even in the context of the minimal version of the model ͑minimal in the sense that no new symmetries or fields are introduced͒.In that model in the lepton sector the charged physical mass eigenstates ͑unprimed fields͒ are related to the weak eigenstates ͑primed fields͒ through unitary transformationsT . It means that the doubly charged vector bilepton, U ϩϩ , interacts with the charged leptons through the current given bywhere g 3l is the SU(3) coupling constant and K is the unitary matrix defined as KϭE R T E L in the basis in which the interactions with the WIn the theoretical calculations of the M →M transition induced by a doubly charged vector bilepton so far only the case Kϭ1 has been considered ͓4͔. Although this is a valid simplification, it does not represent the most general case in the minimal 3-3-1 model. In fact, in that model in the quark sector all left-handed mixing matrices survive in different places of the Lagrangian density ͓5͔. In the lepton sector both left-and right-handed mixing matrices survive in the interactions with the doubly charged vector bilepton as in Eq. ͑2͒ and also with neutral, doubly and singly charged scalars ͑see below͒. Hence, these mixing matrices such as K in Eq. ͑2͒ have the same status as the Kobayashi-Maskawa mixing matrix in the context of the standard model in the sense that they must be determined by experiment. In Ref.͓1͔ it is recognized that their bound is valid only for the flavor diagonal bilepton gauge boson case, i.e., Kϭ1. If nondiagonal interactions, like in Eq. ͑2͒, are assumed, the new upper limit on the conversion probability in the M →M system impliesIf ͉K ͉͉K ee ͉Ϸ0.70, we get a lower bound of 600 GeV for the doubly charged bilepton which is compatible with the upper bound obtained by theoretical arguments ͓6͔.The following is more important. In addition to the contribution of the vector bileptons there are also the doubly charged and the neutral scalar ones. To consider only the vector bileptons is also a valid approximation since all the lepton-scalar couplings can be small if all vacuum expectation values ͑VEVs͒, except the one controlling the SU(3) breaking, are of the order of the electroweak scale and if there is no flavor chan...