Abstract. This contribution is concerned with the nonlinear behavior of a relativistic laser pulse focused in an underdense plasma and with the subsequent generation of fast electrons. Specifically, we study the interaction of laser pulses having their intensity I 2 in the range [10 19 , 10 20 ] W/cm 2 m 2 , focused in a plasma of electron density n 0 such that the ratio n 0 /n c lies in the interval [10 −3 , 2 × 10 −2 ], n c denoting the critical density; the laser pulse power P L exceeds the critical power for laser channeling P ch . The laserplasma interaction in such conditions is investigated by means of 3D Particle in Cell (PIC) simulations. It is observed that the laser front gives rise to the excitation of a surface wave which propagates along the sharp boundaries of the electron free channel created by the laser pulse. The mechanism responsible for the generation of the fast electrons observed in the PIC simulations is then analyzed by means of a test particles code. It is thus found that the fast electrons are generated by the combination of the betatron process and of the acceleration by the surface wave. The maximum electron energy observed in the simulations with I 2 = 10 20 W/cm 2 m 2 and n 0 /n c = 2 × 10 −2 is 350 MeV.The interaction of high-energy laser pulses at relativistic intensities with underdense plasmas is an important area of research, for the studies of the fundamental aspects of the relativistic laser-plasma interaction physics, for its physical applications [1] in particle acceleration and in radiation sources, and for the fast ignition scenario [2] of the inertial confinement fusion. Several experiments, including some very recent ones [3,4] on the propagation of sub-picosecond and picosecond pulses in gas jet plasmas, have motivated the examination of basic nonlinear physical processes such as relativistic selffocusing [5], self-modulation and induced focusing [6], laser pulse channeling [7] and channel stability [8], surface wakes [9] and the electron acceleration in the evacuated channels [10]. We have studied all these processes by means of 3D PIC simulations and analytical theory.We made extensive 3D simulations for an incident laser beam characterized by the initial FWHM w 0 = 10 m, laser intensity I = 5 × 10 19 W/cm 2 , focused in a plasma of density n 0 = 10 −3 n c along the z-direction; the laser field was linearly polarized along the x-direction, its wavelength 0 was 0 = 1 m, and n c denotes the corresponding critical density. With these parameters, the laser beam power is 28 TW, and the ratio P L /P ch is P L /P ch = 1.6; P L and P ch = 1.09 P c denote the incident laser wave power and the power threshold for channeling, respectively, P c being the usual critical power for self-focusing. Figure 1 presents the numerical results obtained with the following parameters: laser pulse duration L = 400 fs, physical time sim corresponding to the PIC simulations sim = 2200 fs.In this regime, the full electron evacuation takes place very rapidly, leading to the formation of a chann...