  We consider a second order singularly perturbed boundary value problem, of
reaction-convection-diffusion type with two small parameters, and the
approximation of its solution by the $hp$ version of the Finite Element Method
on the so-called {\emph{Spectral Boundary Layer}} mesh. We show that the method
converges uniformly, with respect to both singular perturbation parameters, at
an exponential rate when the error is measured in the energy norm. Numerical
examples are also presented, which illustrate our theoretical findings.
