In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case where the input and output operators are collocated. the systems may have an infinite number of poles, and zeros on the imaginary axis. In the case where only position feedback is available, a parallel compensator is effective. The stabilizer is constructed by an adaptive p-controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stsbility of the closed-loop system is proved by LaSalle's invariance pronciple under compactness of the resolvent.