The Rayleigh Nonlinear Oscillation Equation Phenomenon disturbed by two external harmonic forces, one of which is small, will be discussed. Using the Multiple Scales method to obtain analytical solutions, several cases of resonance are determined. Steady-state solutions and their stabilities will be investigated. Depending on the value of amplitudes and frequencies of the external forces given, for a non-trivial steady-state solution, there are two possibilities, namely a periodic solution, and a non-periodic solution that raises the beating phenomenon.