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We construct an infinite family of imaginary bicyclic biquadratic numberfields $k$ with the 2-ranks of their 2-class groups are $\geq3$, whose stronglyambiguous classes of $k/Q(i)$ capitulate in the absolute genus field $k^{(*)}$,which is strictly included in the relative genus field $(k/Q(i))^*$ and westudy the capitulation of the $2$-ideal classes of $k$ in its quadraticextensions included in $k^{(*)}$.

On the strongly ambiguous classes of $k/Q(\sqrt{-1})$ where $k= Q(\sqrt{2p_1p_2},\sqrt{-1})$