Turbulent premixed propane-air flames in the reaction-sheet regime are examined on a cylindrical burner. A two-color, four-beam laser Doppler velocimetry (LDV) system and a three-element electrostatic probe are employed to simultaneously measure gas velocities and flame-front movement at two positions in a turbulent flame brush, one on the centerline and the other off axis. Differences in results that depend on whether flamelets traverse the measurement volume in the burned-to-unburned or unburned-to-burned direction are recorded for the first time. On the centerline, velocity vectors of the flame-front movement are distributed symmetrically with respect to the burner axis, irrespective of the direction of flamelet passage, as they must be by symmetry, but off axis these vectors are directed mainly toward the burner axis when the flame front passes in the unburned-to-burned direction and away from the burner axis when it passes in the burned-to-unburned direction. When the front passes in the burned-to-unburned direction, the axial component of gas velocity is smaller in the unburned mixture, but when it passes in the unburned-to-burned direction, this component is smaller in the burned gas. On the centerline, the radial component of gas velocity increases in the direction opposite that of the flamelet motion, but off axis it always increases in the direction away from the burner axis. In the burned gas, ramps are seen in the LDV traces of the upward component of gas velocity, which continually increases with time between the times of flamelet passage. It is suggested that these burner-stabilized turbulent flames are composed of approximately vertical flamelets having roughly sinusoidal shapes, rapidly moving upward while moving back and forth more slowly, and passing the measuring position alternately in the burned-to-unburned then unburned-to-burned directions. This is explained to be the origin of the relevant aspects of the gas-velocity change across each flame front. It is also suggested that buoyancy may play a role in the observed ramps.