  The existence of at least two homogeneous geodesics in any homogeneous
Finsler manifold was proved in a previous paper by the author. The examples of
solvable Lie groups with invariant Finsler metric which admit just two
homogeneous geodesics were presented in another paper. In the present work, it
is shown that a homogeneous Finsler manifold with indefinite Killing form
admits at least four homogeneous geodesics. Examples of invariant Randers
metrics on Lie groups with definite Killing form admitting just two homogeneous
geodesics and examples with indefinite Killing form admitting just four
homogeneous geodesics are presented.
