We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on S n × T m , where T m is a torus of dimension m ≥ 2 and S n is a sphere of dimension n ≥ 4 . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.