In the experiment, bubbles were generated from two brass nozzles with inner diameters of 1.1 mm. They were submerged in the glass tank filled with distilled water. There have been measured the air pressure fluctuations and the signal from the laser-phototransistor sensor. For analysis of the pressure signal the correlation (the normalized cross - correlation exponent) and non-linear analyses have been used. It has been shown that hydrodynamic interactions between bubbles can lead to bubble departure synchronization. In this case the bubble departures become periodic. The results of calculation of correlation dimension and the largest Lyapunov exponent confirm that hydrodynamic bubble interactions observed for 4 mm spacing between nozzels cause the periodic bubble departures from two neighbouring nozzles.