An ad hoc grid is a wireless heterogeneous computing environment without a fixed infrastructure. This study considers wireless devices that have different capabilities, have limited battery capacity, support dynamic voltage scaling, and are expected to be used for eight hours at a time and then recharged. To maximize the performance of the system, it is essential to assign resources to tasks (match) and order the execution of tasks on each resource (schedule) in a manner that exploits the heterogeneity of the resources and tasks while considering the energy constraints of the devices. In the single-hop ad hoc grid heterogeneous environment considered in this study, tasks arrive unpredictably, are independent (i.e., no precedent constraints for tasks), and have priorities and deadlines. The problem is to map (match and schedule) tasks onto devices such that the number of highest priority tasks completed by their deadlines during eight hours is maximized while efficiently utilizing the overall system energy. A model for dynamically mapping tasks onto wireless devices is introduced. Seven dynamic mapping heuristics for this environment are designed and compared to each other and to a mathematical bound. © 2008 IEEE.