Summary We consider two-armed clinical trials in which the response and/or the covariates are observed on either a binary, ordinal, or continuous scale. A new general nonparametric (NP) approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects. The relative effect is defined by the probability of observing a higher response in the experimental than in the control arm. The notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data. For a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability, respectively. An unbiased and consistent NP estimator for the relative effect is presented. Further, we suggest a NP procedure for correcting the relative effect for covariate imbalance and random covariate imbalance, yielding a consistent estimator for the adjusted relative effect. Asymptotic theory has been developed to derive test statistics and confidence intervals. The test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates. It is shown that the test statistic can be used to evaluate the treatment effect in the presence of (random) covariate imbalance. Approximations for small sample sizes are considered as well. The sampling behavior of the estimator of the adjusted relative effect is examined. We also compare the probability of a type I error and the power of our approach to standard covariate adjustment methods by means of a simulation study. Finally, our approach is illustrated on three studies involving ordinal responses and covariates.