In [6] proof tableau formulations were given of the implication/negation fragments of the important zero-order relevant logics E and R and the semirelevant logic RM . The main purpose of this paper then, is to extend results by giving proof tableau formulations of the distribution-free fragments of E, R and RM and of their first order extensions EQ, RQ and RMQ. Where X is one of these logics, we shall follow [13] in calling its distribution-free fragment OX – the ‘O’ (...) standing for ‘ortho’ which is meant to signify the kinship of these logics to quantum logics or ortho-logics as they now tend to be known. Hence in what follows we shall refer to the logics OX simply as relevant ortho-logics. (shrink)