We present experiments involving oscillating droplets in aqueous cyclodextrin-surfactant solutions. In these experiments, α-cyclodextrin (αCD) and anionic surfactants exhibit remarkable viscoelasticity at the liquid/air interface, with dilatational modulus varying across orders of magnitude. This rheological response depends on the concentrations of different complexes in the solution, particularly of the 2 : 1 inclusion complexes formed by two αCD molecules (αCD2), and one surfactant (S). We propose a model that describes the distribution of these complexes on the droplet surface using a free energy approach, accounting for dipole-dipole interactions. The results of the model reproduce the interfacial behavior of the viscoelastic modulus and phase shift in excellent agreement with the data, clearly indicating that dipole-dipole interactions determine and control the viscoelastic properties of the drops.