The theories of massive and massless chiral superfields and real scalar superfields in an external supergravity are considered. The Schwinger-DeWitt representation for superpropagators of these theories is obtained and the general structure of these objects is investigated. The two first coefficients of the asymptotical expansion of the superpropagators over proper time are calculated in an explicitly covariant way. The divergences of the effective action for the theories under consideration are obtained. The one-loop counterterms for the Wess-Zumino model coupled with external supergravity are calculated. The superconformal anomalies for the theories under consideration are obtained. © 1986.