The American cockroach has three life stages: the egg, a variable number of nymphal instars, and the adult. The life cycle from egg to adult averages about 600 days and the adult life span may be another 400 days.The nymphs emerge from the egg case after about six to eight weeks and mature in about six to twelve months.he life cycle from egg to adult averages about 600 days and the adult life span may be another 400 days. The nymphs emerge from the egg case after about six to eight weeks and mature in about six to twelve months.