Based on the generalized Kalman-Yakubovich-Popov lemma,the positive realness and bound realness lemma for singularly perturbed system in a finite frequency band is studied.It is shown that the positive real property of the full-order system can be deduced from the positive real property of its slow and fast subsystems.The same has been shown for the bounded real property.As an application,a model reduction design scheme is given which is balanced at the low and fast frequency respectively.