  The nonsingular real plane algebraic curves of given degree $d$ are
considered either up to isotopy or up to deformation. The asymptotic behavior
of the number $I_d$ of isotopy classes and the number $D_d$ of deformation
classes are studied. It is shown, in particular, that $log I_d\asypt d^2$.
Other related problems and their higher dimensional generalisations are
discussed.
