Competitive adsorption Of a neutral amphiphilic polymer, namely poly(ethylene oxide) (PEO) and an ionic surfactant, i.e., sodium dodecyl sulfate (SDS), is investigated at the free water surface by computer simulation methods at 298 K. The sampled equilibrium configurations are analyzed in terms of the novel identification of the truly interfacial molecules (ITIM) method, by which the intrinsic surface of the aqueous phase (Le., its real surface corrugated by the capillary waves) instead of an ideally flat surface approximating its macroscopic surface plane, can be taken into account. In the simulations, the surface density of SDS is gradually increased from zero up to saturation, and the structural, dynamical, and energetic aspects of the gradual squeezing out of the PEO chains from the surface are analyzed in detail. The obtained results reveal that this squeezing out occurs in a rather intricate way. Thus, in the presence of a moderate amount of SDS the majority Of the PEO monomer units, forming long bulk phase loops in the absence of SDS, are attracted to the surface of the solution. This synergistic effect of SDS of moderate surface density on the adsorption of PEO is explained by two factors, namely by the electrostatic attraction between the ionic groups of the surfactant and the moderately polar monomer units of the polymer, and by the increase of the conformational entropy of the polymer chain in the presence of the surfactant. This latter effect, thought to be the dominant one among the above two factors, also implies the formation of similar polymer/surfactant complexes at the interface than what are known to exist in the bulk phase of the solution. Finally, in the presence of a large amount of SDS the more surface active surfactant molecules gradually replace the PEO monomer units at the interfacial positions, and squeezing out the PEO molecules from the surface in a monomer unit by monomer unit manner.