Two exemplary exothermic processes, synthesis of nitroglycerine in a continuous stirred tank reactor (CSTR) and synthesis of the explosive RDX in a CSTR, are used to demonstrate the dangers of ignoring the system dynamics when defining criteria for thermal criticality or runaway. Stability analyses are necessary to prescribe such criteria, and for these systems prove the presence of dangerous oscillatory thermal instability which cannot be detected using the steady state thermal balances. (C) 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.