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Multi-agent systems are ubiquitous in the real-world and have received an increasing attention by many researchers worldwide. A multi-agent system is composed of many agents interconnected by a communication network. This paper aims to further investigate the flocking and preserving connectedness in multi-agent nonholonomic systems with proximity graphs, in which the positions and the relative distances are not available to the distributed controllers. Several sufficient conditions are derived to resolve the above problem based on the kinematic model and the dynamic model, respectively. These sufficient conditions indicate that, for any given distinct initial positions and connected initial graph, there always exist gains of the linear protocols to preserve the connectedness of the graph and realize flocking. Moreover, under an additional condition on initial heading angles, the similar result is obtained for a nonlinear protocol with the form of Kuramoto model. Finally, numerical simulations are given to validate the above theoretical results.