The first and fifth Harmonic indices for simple connected molecular graph G have been introduced as and , where . The aim of this paper is computing the Harmonic indices for polyhex zigzag TUZC6[m,n] Nanotube and Nanotori. We calculate the first and the fifth harmonic indices for planar polyhex zigzag nanotube PTUZC6[m,n] and polyhex zigzag nanotube TUZC6[m,n].