(eng): A necessary and su cient condition for reducibility of multi-input multi-output nonlinear delta dierential system is given in terms of the greatest common left divisor of two delta dierential polynomial matrices, associated with the set of the input-output (i/o) equations of the system, dened on a homogenous time scale. This condition provides a basis for system reduction, i.e. for nding the transfer equivalent minimal irreducible representation of the set of the i/o equations.