Spectra of the variance of horizontal velocities derived from the trajectories of superpressure altitude-controlled balloons have been obtained in the frequency range 0.005 to 0.5 cy min−1. With the aid of other constant-altitude balloon data, a spectrum of velocity variance of the upper tropospheric winds is proposed for a range of frequencies termed mesoscale, which is meant to describe scales of motion just smaller than synoptic scale but larger than the motions usually referred to as turbulence. The mesoscale spectra all decreases sharply with frequency at frequencies just above synoptic scale to a frequency of about 0.1 cy min−1, where an irregular increase sets in. The spectra continue to rise to the highest frequencies analyzed, pointing to a second spectral maximum in the turbulent regime. The spectra have been used to estimate the non-representative mesoscale standard deviation of the upper winds of 7 to 17 knots. A horizontal diffusivity by mesoscale motions is estimated to be of the order of 102 cm2 see−1.