Conformal predictors are usually defined and studied under the exchangeability assumption. However, their definition can be extended to a wide class of statistical models, called online compression models, while retaining their property of automatic validity. This paper is devoted to conformal prediction under hypergraphical models that are more specific than the exchangeability model. Namely, we define two natural classes of conformity measures for such hypergraphical models and study the corresponding conformal predictors empirically on benchmark LED data sets. Our experiments show that they are more efficient than conformal predictors that use only the exchangeability assumption.