  M. Busaniche, R. Cignoli, C. Tsinakis and A. M. Wille showed that every
residuated lattice induces a residuation on its full twist product. For their
construction they used also lattice operations. We generalize this problem to
left-residuated groupoids which need not be lattice-ordered. Hence, for the
full twist product we cannot use the same construction. We present another
appropriate construction which, however, does not preserve commutativity and
associativity of multiplication. Hence we introduce so-called operator
residuated posets to obtain another construction which preserves the mentioned
properties, but the results of operators on the full twist product need not be
elements, but may be subsets. We apply this construction also to restricted
twist products and present necessary and sufficient conditions under which we
obtain a pseudo-Kleene operator residuated poset.
