We introduce and study a class of over-the-counter market models specified by systems of Ordinary Differential Equations (ODE's), in the spirit of Duffie-Gârleanu-Pedersen Duffie et al. (Econometrica 73(1):1815-1847, 2005). The key innovation is allowing for multiple assets. We show the existence and uniqueness of a steady state for these ODE's.