This paper concerns items that consist of several item steps to be responded to sequentially. The item score X is defined as the number of correct responses until the first failure. Samejima's graded response model states that each step h =1,..., m is characterized by a parameter b h , and, for a subject with ability θ , Pr( X ≥ h; θ ) = F ( θ − b h ). Tutz's general sequential model associates with each step a parameter dh , and it states that Pr( X ≥ h ; θ )=Π r=1 h G ( θ − d r ). Tutz's (1991, 1997) conjectures that the models are equivalent if and only if F ( x )= G ( x ) is an extreme value distribution. This paper presents a proof for this conjecture.