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 , ,  and  in which Hamilton and Finsler spaces are examined, further [3-9], where generalized Hamilton spaces are studied;  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 . Here, the Zermello's conditions are given in Lagrange-Hamilton spaces, introduced in  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.