Cortical areas are characterized by forward and backward connections between adjacent cortical areas in a processing stream. Within each area there are recurrent collateral connections between the pyramidal cells. We analyze the properties of this architecture for memory storage and processing. Hebb-like synaptic modifiability in the connections and attractor states are incorporated. We show the following: (1) The number of memories that can be stored in the connected modules is of the same order of magnitude as the number that can be stored in any one module using the recurrent collateral connections, and is proportional to the number of effective connections per neuron. (2) Cooperation between modules leads to a small increase in memory capacity. (3) Cooperation can also help retrieval in a module that is cued with a noisy or incomplete pattern. (4) If the connection strength between modules is strong, then global memory states that reflect the pairs of patterns on which the modules were trained together are found. (5) If the intermodule connection strengths are weaker, then separate, local memory states can exist in each module. (6) The boundaries between the global and local retrieval states, and the nonretrieval state, are delimited. All of these properties are analyzed quantitatively with the techniques of statistical physics.