The analysis of whole engine rotor-dynamic models is an important element in the design of aerojet
engines. The models include gyroscopic effects and allow for rubbing contact between rotor and stator
components such as bladed discs and casing. Due to the non-linearities inherent to the system, bifurcations
in the frequency response may arise. Reliable and efficient methods to determine the bifurcation points
and solution branches are required. For this purpose a multi-harmonic balance approach is presented that
allows a numerically efficient detection of bifurcation points and the calculation of both continuous and
isolated branches of the frequency response functions. The method is applied to a test-case derived from a
commercial aero-engine. A bifurcation structure with continuous and isolated solution branches is observed
and studied in this paper. The comparison with time-marching based on simulations shows both accuracy
and numerical efficiency of the newly developed approach