The stability characteristics of a cantilever beam, with and without an intermediate support, subjected to a dynamic terminal moment, is investigated. The moment is assumed to be proportional to the slope of a point along the length of the beam. The proportionally constant, which can be positive or negative, is varied to find the critical stability point. In the absence of intermediate support, stability is lost through divergence when the dynamic moment is proportional to the positive slope, and through flutter when the dynamic moment is proportional to the negative slope. In contrast, the nature of instability switches between divergence and flutter, and between different flutter instability modes while undergoing flutter, in the presence of an intermediate support.