We propose a general class of agreement coefficients for categorical and continuous responses. An agreement coefficient is used to measure the interrater agreement. Motivated by the traditional Cohen’s kappa, concordance correlation coefficient (CCC), and the recent random marginal agreement coefficient (RMAC), we formulate this task using a parameter a, which reflects the distance between marginal distributions. Our approach generalizes Cohen’s kappa as the upper bound and RMAC as the lower bound for categorical data, and generalizes Lin’s CCC as the upper bound and RMAC as the lower bound for continuous data, in a class of appropriate measurements of interrater agreement based on the discrepancy of marginal distributions. We study the large sample properties for the estimators of members of this class and conduct simulation studies to assess and compare the accuracy and precision of the estimators. Some real data examples are also discussed to demonstrate their use.