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 GPDOL (a class of deterministic GL systems) systems L[ m1, m2, ??? mj] and L[ n1, n2, ??? nk] are e-quivalent, iff k = j and there exists a common divisor g of all mi and a common divisor h of all nj such that (?) i: mi/g = nj/h. 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 GPDOL (a class of deterministic GL systems) systems L [m1, m2, ??? mj] and L [n1, n2, ??? nk] are e -quivalent, iff k = j and there exists a common divisor g of all mi and a common divisor h of all nj such that (?) i: mi / g = nj / h.