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RNA mole ules are sequen es of nu leotides that serve as more than mere intermediaries between DNA and proteins, e.g. as atalyti mole ules. Computational predi tion of RNA se ondary stru ture is among the few stru ture predi tion problems that an be solved satisfa tory in polynomial time. Most work has been done to predi t stru tures that do not ontain pseudoknots. Allowing pseudoknots introdu e modelling and omputational problems. In this paper we onsider the problem of predi ting RNA se ondary stru ture when ertain types of pseudoknots are allowed. We rst present an algorithm that in time O(n) and spa e O(n) predi ts the se ondary stru ture of an RNA sequen e of length n in a model that allows ertain kinds of pseudoknots. We then prove that the general problem of predi ting RNA se ondary stru ture ontaining pseudoknots is NPomplete for a large lass of reasonable models of pseudoknots.