  We discuss resonance properties in three-body systems, with examples on
$^{12}{\rm C}$ and $^{24}{\rm Mg}$. We use a microscopic cluster model, where
the generator coordinate is defined in the hyperspherical formalism. The
$^{12}{\rm C}$ nucleus is described by an $\alpha+\alpha+\alpha$ structure,
whereas $^{24}{\rm Mg}$ is considered as an $^{16}{\rm O}+\alpha+\alpha$
system. We essentially pay attention to resonances. We review various
techniques which may extend variational methods to resonances. We consider
$0^+$ and $2^+$ states in $^{12}{\rm C}$ and $^{24}{\rm Mg}$. We show that the
r.m.s. radius of a resonance is strongly sensitive to the variational basis.
This has consequences for the Hoyle state ($0^+_2$ state in $^{12}{\rm C}$)
whose radius has been calculated or measured in several works. In $^{24}{\rm
Mg}$, we identify two $0^+$ resonances slightly below the three-body threshold.
