A particle-core Hamiltonian is used to describe the lowest parity partner bands K π = 1/2 ± in 237 U and 239 Pu. The quadrupole and octupole boson Hamiltonian associated to the core is identical to the one previously used for the description of four positive and four negative parity bands in the neighboring even-even isotopes. The single particle space for the odd nucleon consists of three spherical shell model states, two of positive and one of negative parity. The particle-core Hamiltonian consists of four terms: a quadrupole-quadrupole, an octupole-octupole, a spin-spin and a rotationalÎ 2 interaction, withÎ denoting the total angular momentum. The parameters involved in the particle-core coupling Hamiltonian were fixed by fitting four particular energies in the two bands. The calculated excitation energies are compared with the corresponding experimental data as well as with those obtained with other approaches. Also, we searched for some signatures for a static octupole deformation in the considered odd isotopes.PACS numbers: 21.10. Re,21.60.Ev,27.80.+w,27.90.+b The coherent state model (CSM)[1] describes in a realistic fashion three interacting bands, ground, beta and gamma, in terms of quadrupole bosons. The formalism was later extended [2,3,4,5,6,7] by considering the octupole degrees of freedom. The most recent extension describes eight rotational bands, four of positive and four of negative parity. Observables like excitation energies, intraband E2 and interband E1, E2 and E3 reduced transition probabilities have been calculated and the results were compared with the corresponding experimental data. The formalism works well for both near spherical and deformed nuclei excited in low and high angular momentum states. Indeed, we considered all states with J ≤ 30 in both, the positive and the negative parity bands. Signatures for a static octupole deformation in ground as well as in excited bands have been pointed out in several even-even nuclei.The aim of this paper is to extend CSM for the evenodd nuclei which exhibit both quadrupole and octupole deformation. Thus, we consider a particle-core Hamiltonian:where H sp is a spherical shell model Hamiltonian associated to the odd nucleon, while H core is a phenomenological Hamiltonian which describes the collective motion of the core in terms of quadrupole and octupole bosons. This term is identical to that used in Ref.[7] to describe eight rotational bands in even-even nuclei. The two subsystems interact with each other by H pc , which has the following expression:b † λµ denotes the components of the λ-pole (with λ=2,3) boson operator. The term j J is similar to the spin-orbit interaction from the shell model and expresses the interaction between the angular momenta of the odd-particle and the core. The last term is due to the rotational motion of the whole system, I denoting the total angular momentum of the particle-core system. The core states are described by eight sets of mutually orthogonal functions, obtained by projecting out the angular momentum ...