  We apply the smaller alignment index (SALI) method for distinguishing between
ordered and chaotic motion in some simple conservative dynamical systems. In
particular we compute the SALI for ordered and chaotic orbits in a 2D and a 4D
symplectic map, as well as a two--degree of freedom Hamiltonian system due to
H\'{e}non & Heiles. In all cases, the SALI determines correctly the nature of
the tested orbit, faster than the method of the computation of the maximal
Lyapunov characteristic number. The computation of the SALI for a sample of
initial conditions allows us to clearly distinguish between regions in phase
space where ordered or chaotic motion occurs.
