Amphotericin B (AmB) is a well-known polyene antibiotic used to treat systemic fungal infections. It is commonly accepted that the presence of sterols in the membrane is essential for the AmB biological activity, that is, for the formation of transmembrane ion channels. The selective toxicity of AmB for fungal cells is attributed to the fact that it is more potent against fungal cell membranes containing ergosterol than against the mammalian membranes with cholesterol. According to the "primary complex" hypothesis, AmB associates with sterols in a membrane to form binary complexes, which may subsequently assemble into a barrel-stave channel. To elucidate the molecular nature of the AmB selectivity for ergosterol-containing membranes, in the present work, we used computational methods to study the formation of the putative AmB/sterol complexes in a lipid bilayer. The free energy profiles for the AmB-sterol association in phospholipid bilayers containing 30 mol % of sterols were calculated and thoroughly analyzed. The results obtained confirm the formation of specific AmB/ergosterol complexes and are used to determine the energetic and structural origin of the enhanced affinity of AmB for ergosterol than for cholesterol. The significance of this affinity difference for the mechanism of action of AmB is discussed. The data obtained allowed us also to suggest a possible origin of the increased selectivity of a novel class of less toxic AmB derivatives.