Summary: In a parallel communicating grammar system, several grammars work together, synchronously, on their own sentential forms, and communicate on request. No restriction is imposed usually about the communicated strings. We consider here two types of restrictions, as models of the negotiation process in multi-agent systems: (1) conditions formulated on the transmitted strings, and (2) conditions formulated on the resulting string in the receiving components. These conditions are expressed in terms of regular languages, whose elements the mentioned strings should be. Moreover, we allow that the communicated string is a part (any one, a prefix, a maximal, a minimal one, etc.) of the string of the communicating component. We investigate these variants from the point of view of the generative capacity of the corresponding parallel communicating grammar systems.