Abstract: The talk focuses on some flows of geometric structures. I will present a general result about the well-posedness of geometric flows for non-degenerate differential forms which are parabolic in the direction of closed forms. The result can be applied, in particular, to the Laplacian flow and the Laplacian coflow in G2 geometry and allows one to introduce a generalization of the Calabi flow on balanced manifolds. Moreover, I will discuss the stability of these flows around stationary solutions. Using a similar approach, I will further discuss the stability of the anomaly flow introduced by Phong, Picard and Zhang around some stationary solutions and I will discuss an application to the generalized Ricci flow.