Abstract This paper presents a market equilibrium existence theorem that generalizes and unifies many well-known results. The importance of the theorem is illustrated by applications to large exchange economies. A further extension of Aumann's Existence theorem is obtained which dispenses with the monotony assumption on preferences. In addition the market equilibrium results of Grandmont and Neuefeind are compared. It is shown that the boundary condition of Grandmont's result is equivalent to some natural relaxation of Neuefeind's. In the case of two commodities they are equivalent but for a greater number of commodities Neuefeind's condition is stronger. Journal of Economic Literature Classification Numbers: C62, D51.