  We study conjugate points along homogeneous geodesics in generalized flag
manifolds. This is done by analyzing the second variation of the energy of such
geodesics. We also give an example of how the homogeneous Ricci flow can evolve
in such way to produce conjugate points in the complex projective space
$\mathbb{C} P^{2n+1} = Sp(n+1)/({U}(1)\times{Sp}(n))$.
