Let be a manifold on which a notion of geodesic is defined. (For instance, could be a Riemannian manifold, could be a manifold with affine connection, or could be a Finsler space.)

Two distinct points, and of are said to be conjugate points if there exist two or more distinct geodesic segments having and as endpoints.

A simple example of conjugate points are the north and south poles of a sphere (endowed with the usual metric of constant curvature) -- every meridian is a geodesic segment having the poles as endpoints.