  A new $\alpha$-cluster wave function is proposed which is of the
$\alpha$-particle condensate type. Applications to $^{12}$C and $^{16}$O show
that states of low density close to the 3 resp. 4 $\alpha$-particle threshold
in both nuclei are possibly of this kind. It is conjectured that all
self-conjugate 4$n$ nuclei may show similar features.
