The present study considers a unionised duopoly with the two most popular labour market institutions, i.e. efficient bargaining (EB) and right to manage (RTM) unions and analyses product market stability under quantity competition. By focusing on the role played by labour market institutions on the market dynamics, we show that when the preference of unions towards wages is fairly low, (i) the stability region under RTM is higher than under EB, and (ii) a rise in the union power in the Nash bargaining monotonically increases (reduces) the parametric stability region under RTM (EB). In contrast, when the preference of unions towards wages becomes higher, an increase in the union’s bargaining power acts: (1) as an economic stabiliser when the union power is still low; (2) as an economic de-stabiliser when the union power is already high. These results shed some light on the effects of how labour market structures affect out-of equilibrium behaviours in a duopoly in addition to the many established results on how they affect equilibrium behaviours in such a context, and thus also constitute policy warnings for the design of the labour market institutions as regards the important issue of economic stability.