It is now well ascertained that a variety of instability modes can appear before the conventional plastic limit condition is met. In this note, both flutter and divergence instability modes are investigated. First, the criterion for detecting their occurrence is established, and the case of kinematically constrained discrete systems is investigated. Based on an illustration example, the competition between the occurrences of each of these instability modes is then analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system in hand.