<p>We consider a class of models in even spacetime dimensions 2<i>n</i> which share many similarities with Chern-Simons theories in odd spacetime dimensions 2<i>n</i> + 1. The independent dynamical variables of these models are a GL(2<i>n</i>)-connection and a metric in internal space. The action is a polynomial of degree <i>n</i> in the curvature of the connection, with indices saturated by means of the metric and the Levi-Civita tensor. We show that the theory has no local degree of freedom in 2 spacetime dimensions (<i>n</i> = 1), where it can be reformulated as a constrained <i>BF</i> model, but that its dynamics is more intrincate in higher dimensions (<i>n &gt;</i> 1), where local degrees of freedom are present. We treat in detail the cases of 2 and 4 spacetime dimensions.</p>