Concatenated codes are typically decoded using iterative methods. The sum-product algorithm can be shown to be optimal for cycle-free codes. In this paper two commonly used versions of the sum-product algorithm are investigated with respect to their performance for concatenated codes with cycles. Various serial concatenated codes with an inner accumulator are studied. Simulation results for both update modes are presented for Repeat-Accumulate codes, Accumulate-Repeat-Accumulate codes, and Product-Accumulate codes.