  It is known for a long time that a nonsingular real algebraic curve of degree
2k in the projective plane cannot have more than 7/2*k^2-9/4*k+3/2$ even ovals.
We show here that this upper bound is asymptotically sharp, that is to say we
construct a family of curves of degree 2k such that p/k^2 tends to 7/4$ as k
tends to infinity, where p is the number of even ovals of the curves. We also
show that the same kind of result is valid dealing with odd ovals.
