If a linear, continuous, shift invariant distributed system is considered as a ( dynamical) system converting input signals to output signals, then this information is encapsulated in the impulse response or the transfer function of the system. The set of all transfer functions has the structure of a ring, corresponding to the operations of parallel and cascade connections of two systems. However, in the behavioral theory of Willems, a system is not described in terms of its input-output transformation property. Indeed, the concept of a behavior does not even need the notions of inputs and outputs and is therefore more fundamental than the classical concept of a system given by its transfer function. The question then arises as to what is the structure of the set of all behaviors. This paper argues that the relevant structure here is that of a modular lattice.