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A search for lepton flavour violating decays of a neutral non-standard-model Higgs boson in the $\mu\tau$ and e$\tau$ decay modes is presented. The search is based on proton-proton collisions at a center of mass energy $\sqrt{s}=$ 13 TeV collected with the CMS detector in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The $\tau$ leptons are reconstructed in the leptonic and hadronic decay modes. No signal is observed in the mass range 200-900 GeV. At 95% confidence level, the observed (expected) upper limits on the production cross section multiplied by the branching fraction vary from 51.9 (57.4) fb to 1.6 (2.1) fb for the $\mu\tau$ and from 94.1 (91.6) fb to 2.3 (2.3) fb for the e$\tau$ decay modes.