Abstract. Nanotubical structures are obtained by wrapping a hexagonal grid, and then possibly closing the tube with caps. We show that the asymptotic values of Balaban, sum-Balaban and Harrary indices for nanotubical graphs (open or closed or generalized) are 4.5π(k+l)*n^-1, 4.5(2k+2l)^.5log(1+2^.5) and (k+l)n*log(n), respectively.