Low-dimensional nonnegatively curved fixed-point homogeneous manifolds. Abstract: Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set Fix(M;G). We say that M is fixed point homogeneous if G acts transitively on a normal sphere to some component of Fix(M;G). Fixed point homogeneous manifolds with positive sectional curvature have been completely classified. We will discuss the structure of fi xed point homogeneous Riemannian manifolds with nonnegative curvature and their classification in low dimensions.