In this paper we make an extensive analysis of the imaginary stability of many explicit Runge-Kutta methods with variable coefficients for oscillatory problems. The Runge-Kutta methods considered are based on several construction procedures such as exponential fitting, phase-fitting or dissipative-fitting (the latter two techniques can be combined). Two-dimensional regions of imaginary stability for the first-order test model are obtained. These regions are a generalization of the imaginary stability intervals of classical Runge-Kutta methods. To have an idea of the numerical performance of the methods we have also made a phase-lag and dissipation analysis.