The reaction of phenylacetylene carbonylation to phenyl maleate, phenyl fumarate, and dimethoxylactone in the homogeneous catalytic system PdI2-KI-O-2-NaOAc in methanol solution was found to exhibit oscillations in the redox potential, pH, and rate of gaseous CO-O-2 mixture consumption. This is the first example of an oscillating chemical reaction in typical metal-complex catalysis where a complex organic molecule is formed from simple reactants in solutions of metal complexes. Oscillations were observed for 3.5 h up to 95% conversion of alkyne. The oxidation of CO to CO2 occurs in parallel with carbonylation. The products were analyzed by NMR spectroscopy and GLC coupled with mass spectrometry. The compositions of the gas and liquid phases were controlled by GC and GLC, respectively. The range of NaOAc concentrations within which oscillations were observed was found to be very narrow: from 0 to 0.01 mol/L. It was shown that oxygen transfer through the phase boundary is not a cause of oscillations. The run where PdI2 was replaced by K2Pd2I4 exhibited oscillations similar in shape and amplitude. A reaction scheme was proposed, which includes the processes of Pd(II) reduction to the active catalysts of carbonylation, Pd(I) complexes, followed by the oxidation of palladium(I) complexes by iodine.