This is a work in collaboration with A. Pelczar and C. Rosendal. We give partial answers to the following question by Haskell P. Rosenthal: If a basis $(e_n)$ of a Banach space is such that every block basis of $(e_n)$ has a subsequence equivalent to $(e_n)$, must $(e_n)$ be equivalent to the unit vector basis of $c_0$ or $l_p$, $p \in [1,+\infty)$?