Complete nonorientable minimal surfaces in R3

We consider complete nonorientable minimal immersionsx(M)⊇R ³. Assuming the double coverN ofM has finite total curvature, we generalize an argument of Lopez/Ros to give a sufficient condition for the instability ofx(M) in terms of the total curvature ofM and the genus γ of . We apply this condition to prove that if the immersion is regular thenx(M) is unstable. We also consider the case where the immersion is finitely branched, and we classify the possibilities under the assumption the is hyperelliptic.