This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L systems. We have also defined a classification of GL systems and proved a sufficient and necessary condition for the equivalence of two subclasses of GL systems: two GPD0L (a class of deterministic GL systems) systems L[ m 1 , m 2 ,…, m j ］ and L[ n 1 , n 2 , …, n k ］ are equivalent, iff k = j and there exists a common divisor g of all m i and a common divisor h of all n i such that i : m i / g = n i / h .