Natural oscillations of a spherical interface between a gas and a liquid in a bubble are registered. A possibility of measuring the geometric parameters of stationary and moving particles of the disperse phase by a laser Doppler anemometer is demonstrated. A method for simultaneous determination of the size and velocity of a bubble or a droplet in a two-phase flow is developed. The mean sizes of a group of bubbles settled on a ruler are compared: the results are obtained by two independent methods, i.e., by analyzing the image and by processing the Doppler signal containing information about the natural oscillations of the spherical interface between the media. A possibility of using a laser Doppler anemometer for simultaneous measurements of the velocity and size of bubbles or droplets in a two-phase flow is confirmed.