Measurements of Reynolds-shear-stress spectra in smooth-wall zero-pressure-gradient turbulent boundary layers are presented for four different Karman numbers. The results are plotted using various scaling variables and found to collapse with 'inner-flow' scaling for a modest range of mid-range wavenumbers, the extent of collapse increasing for higher Karman numbers. The results are discussed in light of the attached eddy hypothesis of Townsend (1976)as extended by Perry and Chong (1982). A computation of the cross-power spectra, based upon the same theory, is also presented.