So my professor has taught us that if the Jacobian of the function f of an ODE (t,x)'=f(t,x) evaluated at an stationary point has zero as one of its eigenvalues, then we cannot use the linear approximation to determine its stability.

However, if there are some non-zero eigenvalues (e.g. it's got 3 eigenvalues and only one of them is 0), can I say anything about the stability of the system around such stationary point?