Bifurcation of an invariant torus of a system of differential equations in the degenerate case

We consider a system of ordinary differential equations $\dot x=Lx+X(x,\varepsilon)$, $X(0,\varepsilon)\equiv 0$ in a neighborhood of the equilibrium $x=0$. We give sufficient conditions for bifurcation of an invariant torus in the case when the spectrum of the matrix $L$ consists of zero and purely imaginary eigenvalues and the vector-function $X(x,\varepsilon)$ has the third order of smallness in $x$ and $\varepsilon$ at the origin.