A theory is given to explain the observed dependence on Reynolds number of the decay of turbulent line vortices. It is argued that the turbulent vortex has a triple structure. There is an outer region forr > r 1(r1is the radius of maximum tangential velocity) with a logarithmic distribution of circulation, and forr < r1an inner region and viscous core in both of which the motion is close to solid body rotation. It is predicted thatr1 ∼ (&ngr;&Ggr; 1 t2)1/4, where&Ggr;1is the circulation atr1. Further,&Ggr;1 /&Ggr;0is predicted to be a slowly decreasing function of&Ggr;0/&ngr;, where&Ggr;0is the strength of the vortex. The development of an overshoot of circulation in the outer region is discussed, and the axial velocities produced by growth of a trailing vortex are calculated.