This note outlines conditions under which we can identify a vertical supply model of multiple retailers' and manufacturers' oligopoly-pricing behavior. This is an important question particularly when the researcher believes, contrary to the traditional assumption followed in the empirical literature, that retailers may not be neutral pass-through intermediaries. We show that a data-set of an industry's product prices, quantities, and input prices over time is sufficient to identify the vertical model of retailers' and manufacturers' oligopoly-pricing behavior given nonlinear demand, for homogeneous-products industries, and given multi-product firms, for differentiated-products industries.