In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader-follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-step game of perfect and complete information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. The existence (and uniqueness) problem is complexified in this framework since strategic interactions occur within each partial game but also between both partial games through sequential decisions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the leaders'strategy profile only. Some examples outline our procedure and discuss our assumptions.