Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter of interest and in which the two unknown marginal distributions are the (innnite dimensional) nuisance parameters. The eecient score for can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. In case the family of copula functions corresponds to the normal distributions with mean 0, variance 1, and correlation , the solution of these equations is given, and we thereby show that the Van der Waerden normal scores rank correlation coeecient is asymptotically eecient. We also show that the bivariate normal model with equal variances constitutes the least favorable parametric submodel. Finally, we discuss the interpretation of jj in the normal copula model as the maximum (monotone) correlation coeecient.