The exponential model with pairing attenuation (EMPA) is extended and used to analysis the superdeformed rotational bands(SDRB's) in Thallium nuclei in the mass region A∼190 .The level spins are extracted by fitting the experimental dynamical moment of inertia J(2) to the theoretical version of Harris expansion in even powers of rotational frequency ħω. Using the assigned spins ,the parameters of the extended exponential model are adjusted by using a computer simulated search program to fit the transition energies with experimental ones .The best adopted parameters are used to calculate transition energies Eγ(I) rotational frequencies ħω ,kinematic J(1) and dynamic J(2) moments of inertia .The variation of J(1) and J(2) versus ħω are examined .A staggering functions depends on the concept of EGOS and finite differences are suggested to investigate and exhibit the I=1 staggering effects in transition energies in the studied SDRB's. The phenomenon of identical bands in also investigated in Thallium nuclei.