Abstarct: In this thesis, the electron transport properties in InN and AlN compound semiconductors under an applied weak electric field (104 V/cm) have been studied .Iterative technique was used to solve Boltzmann transport equation. Our results show that in the weak electrical field, the central valley electrons are contributed in the transport of electrons and the inter valley and interband transitions do not exist , while in the strong electric fields, the electrons in the adjacent valleys are contributed in transport and inter valley and interband transitions exist . In fact, when the electric field is strong, the central valley electrons can gain enough energy to go to the other valleys. The Kane's theory has been used in order to investigate the band structure and its effect on electron transport properties. The scattering from the acoustic and polar optical phonons, deformation potential of the lattice, piezoelectric effect and also from ionized impurities have been studied. Moreover, dependence of the electron mobility in terms of temperature and electron concentration in InN and AlN semiconductor systems have been investigated.