We have investigated the electronic properties of zigzag CNTs and BNNTs under the external transverse electric field and axial magnetic field, using tight binding approximation. It was found that after switching on the electric and magnetic fields, the band modification such as distortion of the degeneracy, change in energy dispersion, subband spacing and band gap size reduction occurs. The band gap of zigzag BNNTs decreases linearly with increasing the electric field strength but the band gap variation for CNTs increases first and later decreases (Metallic) or first hold constant and then decreases (semiconductor). For type (II) CNTs, at a weak magnetic field, by increasing the electric field strength, the band gap remains constant first and then decreases and in a stronger magnetic field the band gap reduction becomes parabolic. For type (III) CNTs, in any magnetic field, the band gap increases slowly until reaches a maximum value and then decreases linearly. Unlike to CNTs, the magnetic field has less effects on the BNNTs band gap variation.
