Concurrent programs are difficult to test and debug due to their non-deterministic execution. For deadlocks, traditional deadlock detection algorithms depend on finding cycles in lock graphs created from application programs. This paper first introduces three kinds of blocked relations, lock-blocked, wait-blocked, and join-blocked for Java multi-threaded programs. Previous work does not consider the wait-blocked relations, nor the influence of thread interruption. The paper then proposes two types of deadlocks based on these blocked relations, that is, block-cycle type deadlocks and waiting-block type deadlocks which are acyclic. It also presents an example of implementation to detect these types of deadlocks, and addresses future directions.