We reported a systematic study on the correlated gyrotropic motion of a chain of multiple skyrmions coexistent in an elliptical thin-film ferromagnetic nanodisk. A theoretic model with modified massless Thiele's equations has been set up. The analytical solutions of the model have suggested several gyrotropic eigen modes for the two-skyrmion and three-skyrmion systems with their unique relative configurations among skyrmion cores. Using micromagnetic simulations, we have confirmed the existence of all these analytic modes and their characterized behaviors. In addition, by applying an in-plane exciting magnetic field in the simulations, we exhibited several spin wave modes at higher resonant frequencies with mixing feature of azimuthal and breathing modes.