We present an analysis of the reliability of computation of maximum Characteristic Exponents of Lyapunov from the numerical integrations of asteroid orbits over finite intervals of time. We used two complementary approaches - a comparison of the LCE estimates from the backward and forward integrations of orbits, and a comparison of the estimates coming from the integrations of the same initial conditions over different time spans. The main conclusion is that for a vast majority of asteroids ($> 80\%$) the results can be considered as reliable enough to reveal the very nature and basic properties of the motion.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html