  The spectroscopic properties of the odd-odd isotopes $^{124-132}$Cs have been
studied within the interacting boson-fermion-fermion model based on the
Gogny-D1M energy density functional framework. Major ingredients to build the
interacting boson-fermion-fermion Hamiltonian, such as the
($\beta,\gamma$)-deformation energy surfaces for the even-even core nuclei
$^{124-132}$Xe as well as single-particle energies and occupation probabilities
of the odd nucleons, have been computed microscopically with the constrained
Hartree-Fock-Bogoliubov method. A few coupling constants of the boson-fermion
and residual neutron-proton interactions are fitted to reproduce with a
reasonable accuracy the experimental excitation energy of the low-lying levels
of the odd-mass and odd-odd nuclei. The method is applied to describe the
low-energy low-spin spectra of the odd-odd Cs nuclei and the band structures of
higher-spin higher-energy states, mainly based on the $(\nu
h_{11/2})^{-1}\otimes\pi h_{11/2}$ configuration. Many of those odd-odd Cs
nuclei have been identified as candidates for exhibiting chiral doublet bands.
