High spin states in ¹⁷⁸Ir were investigated by means of in-beam γ-ray spectroscopy techniques using the multidetector array GASP. Excited states of ¹⁷⁸Ir were populated through the ¹⁵⁹Tb(²⁴Mg, 5n) fusion - evaporation reaction at E(²⁴Mg) = 131-141 MeV. Fourteen rotational bands have been observed and their configurations discussed. Alignments, band crossing frequencies, dynamical and kinematical moments of inertia, and electromagnetic properties have been analyzed in the framework of the cranking model. Signature inversion in the πi_13/2 ⊗ νi_13/2 and πh_9/2 ⊗ νi_13/2 structures has been identified and interpreted in the framework of the particle rotor model with residual p-n interaction and variational moment of inertia (VMI). In bands involving the πi_13/2 orbital an increase in the deformation, relative to the other bands, has been found.