State-space exploration is the essence of model checking and an increasingly popular approach for automating test generation. A key issue in exploration of object-oriented programs is handling the program state, in particular the heap. Previous research has focused on standard program execution that operates on one state/heap. We present Delta Execution, a technique that simultaneously operates on several states/heaps. It exploits the fact that many execution paths in state-space exploration partially overlap and speeds up the exploration by sharing the common parts across the executions and separately executing only the "deltas" where the executions differ. We have implemented Delta Execution in JPF, a popular general-purpose model checker for Java programs, and in BOX, a specialized model checker that we have developed for efficient exploration of sequential Java programs. We have evaluated Delta Execution for (bounded) exhaustive exploration of ten basic subject programs without errors. The experimental results show that on average Delta Execution improves the exploration time 10.97x (over an order of magnitude) in JPF and 2.07x in BOX. We have also evaluated Delta Execution for one larger case study with errors, where the exploration time improved up to 1.43x.