The existence of equilibria in economies with infinitely many consumers, producers and commodities is proved in a general structure of the direct system of economies. In the direct system of economies (including overlapping generations economies), the space of agents may not be totally finite, thus, Walras' law and/or total excess demand correspondences may not be well defined. The method of the existence proof is new and direct in the sense that the fixed point argument is applied directly to the inverse limit space of prices without using the finite period truncation method.