[en] We have studied the production of phi mesons in J/psi decays with the Mark III detector at the SPEAR e+e^- storage ring. General features of inclusive phi production are discussed as well as the observation of several exclusive channels containing phi's. From a sample of 2.7 million J/psi's, we have measured the branching ratio of J/psi → phi eta to be (6.8 +- 0.6 +- 0.9) x 10^-4 and that of J/psi → phi eta' to be (3.7 +- 0.6 +- 0.6) x 10^-4. We also present the first observation of the sequential decay J/psi → γ eta c, eta c → phi phi, and we have measured the product branching ratio to be (1.02 +- 0.25 +- 0.14) x 10^-4. The angular distributions of the final state particles in this decay mode give the first experimental determination that the spin and parity of the eta c are 0^-. 50 references, 47 figures