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Abstract Veraverbeke (1977, Stochastic Processes Appl. 5, no. 1, 27-37) and Embrechts and Veraverbeke (1982, Insurance Math. Econom. 1, no. 1, 55-72) obtained that there is a simple asymptotic relation for the ruin probability in the renewal risk model under the assumption that the claim size is heavy tailed. In this note, we point out that the above relation still holds in the delayed renewal risk model.