A thin-layer Navier-Stokes code has been used to compute the turbulent flow over two axisymmetric bodies at transonic speeds and the results are compared to experiment. A critical element of calculating such flows is the turbulence model. Numerical computations have been made with an algebraic eddy viscosity model and the k-epsilon two-equation model. The k-epsilon equations are developed in a general spatial coordinate system and incorporated into the thin-layer, compressible, time dependent Navier-Stokes code. The same implicit algorithm that simultaneously solves the Reynolds-averaged mean flow equations is extended to solve the turbulence field equations using block tridiagonal matrix inversions. Calculations with the k-epsilon model are extended up to the wall and exact values of k and epsilon at the wall are used as boundary conditions.