wheref1 is a number, {a,, a2, a3, } is a sequence of nonzero numbers, and { b1, b2, b3, * } is a sequence of numbers. We obtain conditions necessary and sufficient for (1.1) to converge absolutely, and we indicate their relationship to older sufficient conditions. We find a new characterization of positive definite continued fractions, whose importance is emphasized by the fact (Theorem 4.2) that if (1.1) converges, then there is a positive definite continued fraction which is a contraction of (1.1). We also obtain new sufficient conditions for absolute convergence of positive definite continued fractions.