Article provides an analysis technique for aero-elastic stability of turbines using Hill’s method. It is relevant as it provides an alternative method to the “classical” approach of the multi-blade/Coleman transformation, which is generally implemented to three bladed, symmetrical rotors. This is important as it gives a tool that can be extended to other general cases, such as two bladed (or N-bladed, thus N-degrees of freedom) wind turbines or anisotropic rotors. It is also relevant as the methods used are done within the floating wind turbine stability problem which involves wave periodicity and visits the dynamic stall instability problem which is relevant within the offshore floating wind turbines. Article is very comprehensive and well written!

Specific comments:

On section 4.3, I would show the mathematical procedure to select the principal eigenvalues and corresponding eigenfrequencies as done in section 5.4 for the principal eigenvalues of the Floquet method. Also, section 4.3 only offers the Christensen and Santos, 2005 and Genta,1998 references, vs many more in the Floquet theory section (5.4). If there is room for improvement in that section, that would be very good in my opinion. It would be nice to cite in Skjoldan and Hansen, 2009 in 5.4 if pertinent, since they also give a method to resolve the indeterminacy of modal frequencies in section 2.2.2.

On section 7.1.2 it would be nice to show the mathematical procedure in which the Floquet theory/Hill’s method results are reconstructed into the NR frame, as it is of high significance to interpret the results of these methods on Campbell diagrams, which is being shown by this paper but not necessarily thoroughly explained.

This research article introduces novel aero-elastic stability analysis methods for floating wind turbines. The authors propose an analytical approach using Hill's and Floquet's methods to allow generalization for an n-bladed floating wind turbine system. This approach overcomes the limitation of the Coleman transform, which is typically used in the analysis of three-bladed symmetric wind turbines, but is typically not applicable to otherwise.  The time-domain model used in the study incorporates dynamic stall effects, which are highly relevant for the stability analysis of modern wind turbines. The validation of the proposed methods against the "classical" Coleman transform method shows good agreement. The research article is well-written and highly relevant to the research community.

Minor comments:

Figures 1, 2, 6, 7, 10: Please update the plots to improve readability. Authors could use line styles in addition to, or instead of, colour to distinguish the lines on the plots.  Some of the text labels are also very small and difficult to read.

Sections 7.1.2, 7.2.2, 8.2.1: It is unclear how the results from the rotating frame are expressed in the non-rotating frame.

Section 9: Could the authors comment on how this method can be extended to include additional degrees of freedom such as blade edgewise deflections and tower deflections?