We present experiments and simulations of two mutually mass-coupled biochemical oscillators represented by the nonlinear peroxidase-oxidase reaction. The uncoupled oscillators show simple period-1 (Pi) oscillations of different frequencies for different values of the oxygen concentration in the gas stream. A phase diagram is established where the ratio of the natural frequencies is plotted versus the mass exchange rate. For each frequency ratio four regimes of behavior have been observed for an increasing mass exchange rate : (I) two independent and uncorrelated P1 oscillations; (II) quasiperiodicity in one and P1 oscillations in the other reactor; (III) quasiperiodicity in both reactors; (IV) periodic in-phase synchronization of both reactors. We use the correlation coefficient, the frequencies of the system, and the phase difference between the two cells to characterize the four regimes. A new feature of this work is the experimental observation of an "infinite" modulation period at the transition from the quasiperiodic region to the limit cycle that can be explained by a collision of a torus with a saddle-node bifurcation of a limit cycle (SNIPER bifurcation of codimension two). Simulations using two coupled four-variable DOP models give very good agreement with the experimental results and support our interpretation of the dynamical behavior and the observed bifurcations.