  In this paper, we prove two rigidity results for non-positively curved
homogeneous Finsler metrics. Our first main result yields an extension of
Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove
that every connected homogeneous Finsler space with non-positive flag curvature
and isotropic S-curvature is Riemannian or locally Minkowskian. We extend the
Szab\'{o}'s rigidity theorem for Berwald surfaces and show that homogeneous
isotropic Berwald metrics with non-positive flag curvature are Riemannian or
locally Minkowskian. We prove that a homogeneous $(\alpha, \beta)$-metrics has
isotropic mean Berwald curvature if and only if it has vanishing mean Berwald
curvature generalizing result previously only known in the case of Randers
metrics. Our second main result is to show that every homogeneous
$(\alpha,\beta)$-metric with non-positive flag curvature and almost isotropic
S-curvature is Riemannian or locally Minkowskian.
