In this paper we investigate the relationship between GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework originated in nonequilibrium thermodynamics and the Speed-Gradient (SG) Principle originated in control theory. GENERIC is known as a general structure for the various time-evolution equations for nonequilibrium systems. The SG-principle is successfully used to determine dynamics of entropy-driven systems from the perspective of MaxEnt principle. Based on the SG-principle a time-evolution equations can be derived in a general way. We consider several examples of SG-principle application and show its correspondence to GENERIC framework. The relation between GENERIC and Fokker-Planck equations has already been established by H.C. Öttinger et al. The result of this paper can also be treated to demonstrate the way how Fokker-Planck equations and the SG-principle relate.