  We study the prospects to detect at hadron colliders the Lepton Flavour
Violating Higgs decay H --> tau mu, which can reach substantial branching
fractions in several extensions of the SM. Among them, the generic two higgs
doublet model can be taken as a representative case where B.R.(H --> tau mu)
can reach values of order 10^-1-10^-2. Bounds on the LFV factor kappa_{tau mu}
of order 0.8-1.7 can be derived at 95% c.l. at Tevatron Run-2 with 4 fb^-1 for
m_H = 110-150 GeV.
