It is analytically shown when chaos exists in the behavior of null and
timelike geodesics in the general case of geodesic motion in static a
nd diagonal fields of general relativity. We demonstrate the effective
ness of our method of investigating chaos in the behavior of geodesic
motion in the multi-black-hole spacetimes. An optical model of chaotic
behavior of geodesics in spacetimes with cylindrical symmetry is pres
ented. The Lyapunov characteristic time is defined and estimated for g
eodesic motion of a test particle in the external fields of general re
lativity. We find that its value is positive in some compact regions o
f the configuration space. This means that the trajectories have the p
roperty of local instability which implies the sensitive dependence on
initial conditions.