This paper analyzes the problem of selling a number of indivisible items to a set of unitdemand bidders. An ascending auction mechanism called the Excess Demand Ascending Auction (EDAA) is defined. The main results demonstrate that EDAA terminates in a finite number of iterations and that the exact auction mechanism in Demange, Gale and Sotomayor (J. Polit. Economy 94: 863–872, 1986) and its modification based on the Ford- Fulkerson method, proposed by Sankaran (Math. Soc. Sci. 28: 143–150, 1994), reduce to special cases of EDAA.