When bubbles rise in a vertical turbulent liquid flow, their trajectories are affected by the turbulence. In addition, the motion of the bubbles relative to the liquid causes velocity fluctuations in the latter. This is commonly called “pseudoturbulence.” Over the past decades measurements of pseudoturbulence have been reported (Theofanous and Sullivan, 1982; Lance and Bataille, 1991; Stewart, 1995). For the bubbles used in the majority of these experiments the relative motion can, as far as the rise of isolated bubbles is concerned, be described by potential flow together with thin boundary layers to accommodate the tangential stress difference between liquid and gas. With the help of this same description an approximate calculation is made of the kinetic energy in the pseudoturbulence. Except for a very low gas concentration, this turns out to be much smaller than the measurements indicate. A tentative explanation of this phenomenon is presented, based on the observed behavior (Duineveld, 1994) of bubbles encountering another bubble or a solid wall.