  A general algorithm is presented for estimating the nonlinear instability
threshold, $\sigma_c$, for subcritical transitions in systems where the
linearized dynamics is significantly non-normal (i.e. subcritical bifurcations
of {\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is
presented as an example. The predictions are then compared to numerical studies
with excellent agreement.
