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It is known for a long time that a nonsingular real algebraic curve of degree2k 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 weconstruct a family of curves of degree 2k such that p/k^2 tends to 7/4$ as ktends to infinity, where p is the number of even ovals of the curves. We alsoshow that the same kind of result is valid dealing with odd ovals.

Real plane algebraic curves with asymptotically maximal number of even ovals