In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by [Bala and Goyal, 2000a] and [Bala and Goyal, 2000b] in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the payoff function to find conditions under which Nash networks always exist. We provide two properties--increasing differences and convexity in the first argument of the payoff function that ensure the existence of Nash networks. Note that the commonly used linear payoff function satisfies these two properties.