With traditional testing, the test case has no control over non-deterministic scheduling decisions, and thus errors dependent on scheduling are only found by pure chance. Java Path Finder (JPF) is a specialized Java virtual machine that can systematically explore execution paths for all possible schedulings, and thus catch these errors. Unfortunately, execution-based model checkers, including JPF, cannot be easily adapted to support real-time programs. We propose a scheduling algorithm for JPF which allows testing of Safety Critical Java (SCJ) applications with periodic event handlers at SCJ levels 0 and 1 (without aperiodic event handlers). The algorithm requires that deadlines are not missed and that there is an execution time model that can give best- and worst-case execution time estimates for a given program path and specific program inputs. Our implementation, named R SJ, allows to search for scheduling dependent memory access errors, certain invalid argument errors, priority ceiling emulation protocol violations, and failed assertions in application code in SCJ programs for levels 0 and 1. It uses the execution time model of the Java Optimized Processor (JOP). We test our tool with