A full appreciation of the role played by gasmetallicity (Z), star formation rate (SFR) and stellar mass (M*) is fundamental to understanding how galaxies form and evolve. The connections between these three parameters at different redshifts significantly affect galaxy evolution, and thus provide important constraints for galaxy evolution models. Using data from the Sloan Digital Sky Survey-Data Release 7 (SDSS-DR7) and the Galaxy and Mass Assembly (GAMA) surveys, we study the relationships and dependences between SFR, Z and M*, as well as the Fundamental Plane for star-forming galaxies. We combine both surveys using volumelimited samples up to a redshift of z ≈ 0.36. The GAMA and SDSS surveys complement each other when analysing the relationships between SFR, M* and Z. We present evidence for SFR and metallicity evolution to z ∼ 0.2. We study the dependences between SFR, M*, Z and specific SFR (SSFR) on theM*-Z, M*-SFR, M*-SSFR, Z-SFR and Z-SSFR relations, finding strong correlations between all. Based on those dependences, we propose a simple model that allows usto explain the different behaviour observed between low- and high-mass galaxies. Finally, our analysis allows us to confirm the existence of a Fundamental Plane, for which M* = f(Z, SFR) in star-forming galaxies. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.