The integration of expanders into heat exchanger networks (HENs) is a complex task since both heat and work are involved. In addition, the role of streams (as hot or cold), the utility demand, and the location of pinch points may change. With certain well-defined conditions, four theorems are proposed for the integration of expanders into HENs above ambient temperature with the objective of minimizing exergy consumption. A straightforward graphical methodology for above ambient HENs design including expanders is developed on the basis of Grand Composite Curves (GCCs). It is concluded that to achieve a design with minimum exergy consumption, stream splitting may be applied and expansion should be done at pinch temperatures, hot utility temperature, or ambient temperature. In the majority of cases, however, and in line with the concept of Appropriate Placement from Pinch Analysis, expansion at pinch temperatures gives the minimum exergy consumption. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 3404-3422, 2015