Many significant geometers contributed to the generalization of Riemann spaces in different directions. An almost complete list of them can be found in Miron's books. Here are mention [1], [2], [17] and [18] in which Hamilton and Finsler spaces are examined, further [3-9], where generalized Hamilton spaces are studied; [10] is most connected with the subject, and in [11-16] this problem also appears. Zermello's condition in Miron's $Osc^kM$ was examined in [6]. Here, the Zermello's conditions are given in Lagrange-Hamilton spaces, introduced in [9] and presented at the Workshop on Finsler Geometry 2009, Debrecen. It is proved that for a fundamental function for which the Zermello's conditions are satisfied all energies of higher order are equal to zero.