We introduce a new kind of nonisospectral Lax representation, contact Lax pair, related to contact geometry. The compatibility conditions for the contact Lax pairs yield a broad new class of (3+1)-dimensional integrable systems, thus demonstrating that such systems are considerably less exceptional than it was generally believed.
To illustrate our results, we present, inter alia, a new (3+1)-dimensional integrable system with an arbitrarily large finite number of components. In the simplest special case, this system yields a (3+1)-dimensional integrable generalization of the dispersionless Kadomtsev—Petviashvili equation.