We propose two new asynchronous algorithms for solving Distributed Constraint Satisfaction Problems (DisCSPs). The first algorithm, AFC-ng, is a nogood-based version of Asynchronous Forward Checking (AFC). The second algorithm, Asynchronous Inter-Level Forward-Checking (AILFC), is based on the AFC-ng algorithm and is performed on a pseudo-tree ordering of the constraint graph. AFC-ng and AILFC only need polynomial space. We compare the performance of these algorithms with other DisCSP algorithms on random DisCSPs in two kinds of communication environments: Fast communication and slow communication. Our experiments show that AFC-ng improves on AFC and that AILFC outperforms all compared algorithms in communication load.