A widely-used way to deal with the in-tractability of various deduction problems is based on identifying their tractable cases. Current techniques for this are highly problem specific. We present a new technique that obtains powerful tractability results for many different problems. Our technique is based on a notion of partial consistency for logical theories. Any set of theories for which a fixed level of partial consistency can guarantee log-ical consistency provides a tractable class of deduction problems. We apply this technique to obtain tractability results in the areas of constraint satisfaction problems, databases with incomplete information and disjunctive logic programming.