The densities of states of quasiparticles in isolated flux vortices in clean limit superconductors have been calculated for various kappa , using an extension of calculations by Bardeen et al. (1969). Results similar to the dirty limit calculations of Watts-Tobin et al (1973) were found, with the density per unit length at zero energy varying from 4 pi xi ²n(0) at low kappa to 7 eta xi ²n(0) at kappa =30, where xi is the coherence length and n(0) the one-electron density of states per unit volume at the Fermi surface. Experimental studies of the density N(E) as a function of energy were performed by tunnelling on thin films of Pb, Sn and Al at less than 0.1K. Good agreement was found between the experimental and theoretical reduced densities N(E)/N(0). The absolute magnitude of N(0) was, however, too small by a factor of about 5.