The modeling of bivariate dependence is usually accomplished with symmetric copula models. However, many examples on real datasets show that this hypothesis of symmetry may frequently fail to hold, so there is a need for inferential methods using asymmetric dependence structures. In this paper, useful tools for modeling non-exchangeable dependence structures are developed under a broad class of asymmetric copulas introduced by Khoudraji (1995). A special attention is given to the testing of the composite hypothesis that the underlying copula of a population belongs to this general class of models. The problem of selecting a specific Khoudraji-type copula via goodness-of-fit testing is considered as well, hence providing a complete set of tools for inference when facing bivariate data exhibiting an asymmetric dependence structure. Monte Carlo simulations show that the newly introduced methodologies work well in small and moderate sample sizes. Their usefulness for copula modeling is illustrated on real data sets exhibiting patterns of asymmetric dependence.