COMPLETE NONORIENTABLE MINIMAL-SURFACES IN R3

We consider complete nonorientable minimal immersions x(M) subset-or-equal-to R3. Assuming the double cover N of M has finite total curvature, we generalize an argument of Lopez/Ros to give a sufficient condition for the instability of x(M) in terms of the total curvature of M and the genus-gamma of NBAR. We apply this condition to prove that if the immersion is regular then x(M) is unstable. We also consider the case where the immersion is finitely branched, and we classify the possibilities under the assumption that NBAR is hyperelliptic.