We study the resistance of a block cipher against a class of general attacks which we call  iterated attacks . This class includes some elementary versions of differential and linear cryptanalysis. We prove that we can upper bound the complexity of the attack by using decorrelation techniques. Our main theorem enables us to prove the security against these attacks (in our model) of some recently proposed block ciphers COCONUT98 and PEANUT98, as well as the AES candidate DFC. We outline that decorrelation to the order 2d is required for proving security against iterated attacks of order d