The high-energy behavior of different quantities which are directly measured in neutrino reactions (such as the total cross section, average momentum transfer, etc.) is considered. Strong interactions are assumed to be based on renormalizable field theories. Extending the method used by Zee, Wilczek, and Treiman, it is shown that as a consequence of energy-momentum- tensor conservation the asymptotics of the total neutrino cross section is linear in the case of asymptotically free theory as well as in the case of field theory with fixed point. Definite predictions are also made concerning the asymptotics of Q2, ν. The results obtained lead to the conclusion that within asymptotically free theories the behavior of integral quantities measured in neutrino reactions follows asymptotically that of the corresponding moments from the structure functions.