Suppose $G$ is a graph with the vertex set $V(G)$. A set $D\subseteq V(G)$ is a total k-dominating set if every vertex $v\in V(G)$ has at least $k$ neighbours in $D$. The total $k$-domination number $\gamma_{kt}(G)$ is the size of the smallest total $k$-dominating set. When $k=2$ the total 2-dominating set is referred to as a double total dominating set. In this work we compute the exact values for double total domination number on H-phenylenic nanotubes $HPH(m,n)$, $m,n\geq 2$ and H-naphtalenic nanotubes $HN(m,n)$, $n=2k$, $m,n\geq 2$. As all vertices have a degree 2 or $3$, there is no total $k$-domination for $k \geq 3$ for H-phenylenic and H-naphtalenic nanotubes, and the double total domination is the maximum possible.