We present a molecular-thermodynamic theory of the complexation of nonionic polymers and surfactants in dilute aqueous solutions. The theoretical formulation combines a thermodynamic description of polymer-surfactant solutions with a molecular model of polymer-surfactant complexation. The molecular model of complexation is based on the "necklace model", in which a polymer-surfactant complex is described as composed of a series of spherical micelles with their surfaces covered by polymer segments and connected by polymer strands belonging to the same polymer molecule. The theory incorporates explicitly the effects of (i) solvent quality, (ii) polymer hydrophobicity and flexibility, and (iii) specific interactions between the polymer segments and the surfactant hydrophilic moieties on the complexation behavior. Moreover, the theory also accounts for the competition between repulsive electrostatic interactions between polymer-bound micelles and elastic restoring forces within the polymer chain. The theory can be utilized to predict (I)the critical aggregation concentration (CAC), which signals the onset of polymer-surfactant complexation, (2) the number of micelles bound per polymer chain, (3) the aggregation number of polymer-bound micelles, (4) the average distance between these micelles, and (5) the mean-square end-to-end distance of the complex, as well as the critical micelle concentration (CMC), which signals the onset of micelle formation in the absence of polymers. Our theoretical results indicate that the two dominant driving forces leading to the complexation of nonionic polymers and surfactants are (i) the tendency of the polymer to adsorb at the micellar core-water interface and (ii) the existence of specific attractions between the polymer segments and the surfactant hydrophilic moities. In addition, poor solvent quality and small sizes of the surfactant hydrophilic moieties may also promote complexation. One of our central findings is that polymer-surfactant complexation proceeds via a stepwise association process. In other words, as the surfactant concentration is increased, complexes containing one micelle form first, and only when all the available polymers have one micelle bound to them do complexes containing two micelles begin to form at the expense of those containing one micelle, and so on. The theoretical predictions of the CAC, the CMC, the aggregation number of the polymer-bound micelles, and the number of surfactant molecules bound per polymer chain at binding saturation, for aqueous solutions of poly(ethylene oxide) (PEG) and polyvinylpyrrolidone (PVP) mixed with various sodium alkyl sulfates (with and without added salt), are found to be in reasonable agreement with the available experimental data.