  $J^{\pi}$= 0$^+$ states have been investigated in the actinide nucleus
${}^{240}$Pu up to an excitation energy of 3 MeV with a high-resolution (p,t)
experiment at $E_{p}$= 24 MeV. To test the recently proposed $J^{\pi}$= 0$^+_2$
double-octupole structure, the phenomenological approach of the
spdf-interacting boson model has been chosen. In addition, the total 0$^+$
strength distribution and the $0^+$ strength fragmentation have been compared
to the model predictions as well as to the previously studied (p,t) reactions
in the actinides. The results suggest that the structure of the 0$^+_2$ states
in the actinides might be more complex than the usually discussed pairing
isomers. Instead, the octupole degree of freedom might contribute
significantly. The signature of two close-lying 0$^+$ states below the
2-quasiparticle energy is presented as a possible manifestation of strong
octupole correlations in the structure of the 0$^+_2$ states in the actinides.
