This paper introduces two channel models of correlated parallel channels. Then we analyze structure of error correcting codes over these correlated parallel channels. We derive necessary and sufficient conditions for these codes and some code construction is presented. We also show some upper and lower bounds on the coding rate of the error correcting codes for correlated parallel channels. The introduced channel models are related to burst error channels and the codes analyzed in this paper can be used as asymmetric interleaving codes for burst error channels.