  Newton's problem of the body of minimal aerodynamic resistance is
traditionally stated in the class of {\it convex} axially symmetric bodies with
fixed length and width. We state and solve the minimal resistance problem in
the wider class of axially symmetric but {\it generally nonconvex} bodies. The
infimum in this problem is not attained. We construct a sequence of bodies
minimizing the resistance. This sequence approximates a convex body with smooth
front surface, while the surface of approximating bodies becomes more and more
complicated. The shape of the resulting convex body and the value of minimal
resistance are compared with the corresponding results for Newton's problem and
for the problem in the intermediate class of axisymmetric bodies satisfying the
{\it single impact} assumption \cite{CL1}. In particular, the minimal
resistance in our class is smaller than in Newton's problem; the ratio goes to
1/2 as (length)/(width of the body) $\to 0$, and to 1/4 as (length)/(width)
$\to +\infty$.
