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www.esat.kuleuven.be/˜jwillems Abstract—Behavioral system theory has become a successful framework in providing a viewpoint that does not depend on a priori notions of inputs/outputs. In particular, this theory provides such notions as controllability, without an explicit reference to state space formalism. One also obtains several interesting consequences of controllability, for example, direct sum decomposition of the signal space with a controllable behavior B as a direct summand. While there are some attempts to extend this theory to infinite-dimensional systems, for example, delay systems, the overall picture seems to remains incomplete. This article extends this theory, particularly the notion of controllability, to a well-behaved class of infinite-dimensional systems called pseudorational. A crucial notion in connection with this is the Bézout identity, and we relate a recent result to the context of behavioral controllability. We establish the relationships with such notions as image representation, direct sum decompositions. I