  We construct an infinite family of imaginary bicyclic biquadratic number
fields $k$ with the 2-ranks of their 2-class groups are $\geq3$, whose strongly
ambiguous 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 we
study the capitulation of the $2$-ideal classes of $k$ in its quadratic
extensions included in $k^{(*)}$.
