Abstract We present globally supersymmetric models of gauged scale covariance in ten, six, and four dimensions. This is an application of a recent similar gauging in three dimensions for a massive self-dual vector multiplet. In ten dimensions, we couple a single vector multiplet to another vector multiplet, where the latter gauges the scale covariance of the former. Due to scale covariance, the system does not have a Lagrangian formulation, but has only a set of field equations, like Type IIB supergravity in ten dimensions. As by-products, we construct similar models in six dimensions with N = ( 2 , 0 ) supersymmetry, and four dimensions with N = 1 supersymmetry. We finally get a similar model with N = 4 supersymmetry in four dimensions with consistent interactions that have never been known before. We expect a series of descendant theories in dimensions lower than ten by dimensional reductions. This result also indicates that similar mechanisms will work for other vector and scalar multiplets in space–time lower than ten dimensions.