DQAINF: An algorithm for automatic integration of infinite oscillating tails. The paper describes a quadrature routine designed to integrate a (scalar or vector) function with a certain type of infinite oscillating, decaying tails over an infinite interval. The algorithm is based on the assumption that the oscillating behavior is due to the superposition of periodic functions which change sign when evaluated at points of distance half a period. Hence, following the basic ideas of J. N. Lyness [J. Comp. Appl. Math. 12/13, 109-117 (1985; Zbl 0574.65013)], partitioning the original integral into an infinite series of integrals all of same interval length yields close relations to alternating series, and the Euler transformation (together with some modifications) implies very stable schemes for accelerated approximations. A FORTRAN subroutine for the algorithm is described in detail. Six examples show the efficiency of the method.