Distributed peer-to-peer computing in which no centralized control server is assumed, and in some cases, client-server architecture is actually rejected, has been the subject of intense investigations in the field of information technologies in the recent years. This new paradigm of designing large-scale distributed intelligent systems attracts attention of both researchers and developers of industrial applications. This paradigm provides qualitatively new capabilities, especially for designing systems consisting of a large number of autonomous instances which can appear and disappear from the system at any time instant. The idea of integration of these systems (hereinafter, P2P systems for brevity) and multi-agent technologies is especially attractive; it realizes the advantages of both paradigms, namely, the maturity of technologies and the relative simplicity of creation of multi-agent systems consisting of autonomous intelligent programs which interact via a high-level language, as well as the openness, the scalability, and the reliability of P2P systems. This integration seems quite natural. Indeed, multi-agent systems is the set of autonomous intelligent programs; therefore, the structuring of these programs into the network whose nodes interact directly without any intermediate server is the natural step if the technology of P2P interactions has been well developed using a high level language. However, for practical realization of this idea, it is necessary to make one very important step, namely, to develop mechanisms for agent interaction on a semantic level, when agents query some functionalities (services) from each other, possibly, not knowing a priori what particular agents can provide the queried functionality (service) and whether these agents exist in the network. The application of the agent variant of the architecture, the service oriented architecture, another new paradigm of construction of information systems, provides practical capability of realization of mechanisms of semantic interaction of agents of the open P2P network. This work represents the P2P agent platform developed by the authors whose instances installed on the network nodes above the standard P2P service form the distributed meta-knowledge knowledge base intended for organization of semantic P2P interaction of agents. Application-oriented agents placed on the network nodes above the instances of the agent platform receive the capability of semantic interaction. The program realization of the platform is supported by the mechanism of P2P interaction of agents using messages with standard formats and pair communications of the network nodes. The role, functions, and the essence of the processes of operation of this platform is explained using two applications as the examples; these applications are sufficiently important from the practical point of view. They are used for verification of basic solutions presented in this work.