Reactor designs with a fast neutron spectrum have recently moved into the research focus for possible Generation IV reactor concepts - a representative of which is the molten salt fast reactor (MSFR). In order to assess the safety and reliability of this reactor concept, it is necessary to obtain knowledge of the system behaviour. An important part of this research area are investigations regarding the dynamical stability of the MSFR. Research regarding the MSFR stability so far has either been using linearised models for stability criteria or only been examining certain transients at fixed parameter v alues. This work delivers a comprehensive stability analysis for a non-linearised MSFR model, and a wide range of values for all relevant parameters. For this purpose, a one-dimensional MSFR model was set up, taking neutron kinetics and thermal hydraulics in the form of a system of differential equations into account. The stability of this model was investigated by means of the numerical tool MATCONT, which was used to monitor the evolution of a so-called fixed-point solution, here referring to the steady state at operating conditions of the system, while system parameters got varied. The MATCONT analyses showed no loss of stability for any of the considered parameter variations and no solutions that might co-exist in parallel with the steady-state fixed-point solution. Therefore these results indicate a stable fixed p oint t o w hich a ll s olution t ransients converge, making the considered MSFR model insusceptible to deviations from the equilibrium.