We investigate the context-free languages whose complements are also context-free. We call them strongly context-free languages. The family of strongly linear languages is similarly defined. After examining the closure properties of the family of strongly context-free languages, we prove that any slender context-free language is strongly linear. We then show that there are languages of a bounded complexity in terms of the number of non-terminals or productions necessary to generate them, whereas the complexity of their complements is arbitrarily large.