The structural stability of constrained polynomial differential systems of the form a(x, y)x′+b(x, y)y′=f(x, y), c(x, y)x′+d(x, y)y′=g(x, y), under small perturbations of the coefficients of the polynomial functions a, b, c, d, f and g is studied. These systems differ from ordinary differential equations at ‘impasse points’ defined by ad−bc=0. Extensions to this case of results for smooth constrained differential systems [7] and for ordinary polynomial differential systems [5] are achieved here.