A real matrix is Hurwitz if its eigenvalues have negative real parts. The talk is about the following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS): Let X be a C1 planar vector field whose derivative DX(p) is Hurwitz for almost all point p in the plane. Then the singularity set of X, Sing(X), is either an emptyset, a one-point set or a non-discrete set. Moreover, if Sing(X) contains a hyperbolic singularity then X is topologically equivalent to the radial vector field (x,y)->(-x,-y). This generalises BGAS to the case in which the vector field is not necessarily a local diffeomorphism. Joint work with Roland Rabanal.