Data from long-term multi-frequency monitoring are used to analyze variations in the flux density of the active galactic nucleus S4 0954+658. These data were obtained at the CrimeanAstrophysical Observatory, the Metsähovi Radio Observatory of Aalto University, the University of Michigan Radio Astronomy Observatory, the Cavendish Laboratory of Cambridge University, the Special Astrophysical Observatory, and the National Institute of Astrophysics, Optics, and Electronics; 0.1–300-GeV data from the Fermi space gamma-ray observatory were also used. Radio data at 4.8, 8, 14.5, 15, 22.2, and 36.8 GHz are considered together with optical and near-infrared data in the R, J, H, and K filters. In the framework of a model in which binary supermassive black holes (SMBHs) are present in active galactic nuclei, harmonic and structural analyses are carried out to establish the orbital (Torb ≈ 780 yrs) and precessional (Tpr ≈ 7800 yrs) periods in the rest frame of the source. The development of the most powerful flare ever observed in this object, which occurred in February 2015, is considered. The delay in the flare’s development in different wavelength ranges from the gamma-ray to the radio is determined. both the magnitude of the delays and the durations of the flares themselves suggest that the physical characteristics of S4 0954+658 are similar to those of the blazar S5 0716+714, which displays evidence of a high γ factor for the jet motion and high superluminal speeds in the jet. The masses of the components of the binary SMBH (M and m), the dimensions of their orbit, and the velocity of the lower-mass SMBH about the central SMBH are estimated. The derived physical characteristics are subject to a comparative analysis.