The response of an oscillator with a nonlinear stiffness of the hard‐spring type to narrow band Gaussian random noise is analyzed theoretically by using the method of quasi linearization. The particular point of interest is the possibility of an occurrence of multiple valued response or “jumps” such as one observes when the exciting force is sinusoidal. It is argued that while it does not seem possible to have multivalued response with wide‐band (white noise) excitation, the response to narrow band excitation might exhibit such behavior owing to the temporal correlation of the source with the response. Numerical computations of the response curves do suggest multivalued response. In experiments with a nonlinear oscillator, multivalued response was observed, but agreement between theory and experiment may only be claimed to be qualitative.