We report on the linear and nonlinear rheology of surfactant solutions of elongated wormlike micelles. The surfactant solutions placed under scrutiny are made of cetylpyridinium chloride (CP+, Cl-) and sodium salicylate (Na+, Sal-) diluted in 0.5 M NaCl-brine. Both semidilute and concentrated regimes of entangled micelles were investigated. Rheological experiments were performed at ambient temperature ($T = 25 ~^\circ$C) for surfactant concentrations $\phi = 1\,\%{-}30\,\%$. When submitted to a steady shear high enough (for shear rate $\dot{\gamma}$ typically higher than 1-10 s-1) the solutions of wormlike micelles exhibit a first-order isotropic-to-nematic transition for all surfactant concentrations $\phi\geq 6\,\%$. The transition is characterized by a true plateau in the shear rate dependence of the shear stress $\sigma(\dot{\gamma})$. For $\dot{\gamma}$ above the transition rate $\dot{\gamma}_{\rm I/N}$, σ remains constant at σI/N. In the concentrated regime, the transition is clearly first-order. However, the first-order character weakens upon increasing dilution, suggesting that at some critical concentration φc it becomes second-order. Below φc, the transition ceases to occur : the $\sigma(\dot{\gamma})$-behavior rather indicates a progressive and homogeneous orientation of the micelles throughout the sample. Moreover, in the two-phase domain (where both isotropic and nematic phases coexist) a characteristic transient behavior of the shear stress σ(t ) measured at constant $\dot{\gamma}>\dot{\gamma}_{\rm I/N}$ as a function of time has been observed and investigated in detail. In agreement with the picture of the first-order phase transition (in the domain of metastability), the transient behavior could be interpreted quantitatively in terms of nucleation and one-dimensional growth process. These results are finally compared to recent predictions by Spenley, Cates and MacLeish (Ref. [7]) who described the nonlinear rheology of wormlike micelles in terms of mechanical instability of shear-banding type.