  Consider a flat vector bundle F over compact Riemannian manifold M and let f
be a self-indexing Morse function on M. Let g be a smooth Euclidean metric on
F. Set g_t=exp(-2tf)g and let \rho(t) be the Ray-Singer analytic torsion of F
associated to the metric g_t. Assuming that the vector field $grad f$ satisfies
the Morse-Smale transversality conditions, we provide an asymptotic expansion
for log(\rho(t)) for t\to\infty of the form a_0+a_1t+b log(t)+o(1). We present
explicit formulae for coefficients a_0,a_1 and b. In particular, we show that b
is a half integer.
