The leaderless consensus problem in a class of dynamic agents with high-order input-affine nonlinear models is studied. Based on communication of position information among the agents, an adaptive protocol is proposed that guarantees achieving consensus in the network in the presence of unknown parameters in the agents models. The network topology is considered undirected, which may not be connected constantly. Hence, by invoking the Cauchy convergence criterion, sufficient conditions to achieve consensus in the presence of jointly connected switching topologies are obtained. A numerical example for a team of single-link flexible joint manipulators with forth-order nonlinear models is provided to confirm the accuracy of the proposed consensus protocol. random networks was investigated in [7]. In [8], achieving consensus in networks of first-order agents with jointly connected topologies was studied, and in [9], a consensus protocol for networks of first-order agents in the presence of diverse communication delays was introduced. Because of practical issues, the consensus problem over second-order MASs was studied as well. Indeed, the control inputs of a large number of systems and vehicles are forces or torques, which provide acceleration. Therefore, to describe the behaviors of accelerated agents, it is necessary to consider second-order models. For instance, by using the information of agents relative positions and considering velocity damping terms, the consensus protocol proposed in [6] was extended to second-order MASs under undirected networks in [10]. By considering the information of agents relative velocities, that protocol was extended to directed networks in [11] and [3]. Achieving finite time consensus in second-order MASs in the presence of input saturation was studied in [12], and the consensus problem in networks of second-order MASs with switching topologies was studied in [13].However, in practice, there exist some systems and vehicles that require higher-order differential equations to be modeled. In other words, the input-output relationship in those systems can just be expressed by higher-order differential equations. Therefore, the consensus problem in MASs with high-order models is necessary to be investigated as well. For instance, based on measurement of the relative states of agents and employing local damping terms, the consensus protocols of [11] and [3] were extended to higher-order MASs in [14] and [15]. A dynamic consensus control scheme for high-order MASs was proposed in [16]. Average consensus over high-order MASs was studied in [17]. The H 1 consensus problem for high-order MASs was studied in [18], and a consensus protocol for networks of high-order agents with connected switching topologies and time-varying communication delays was proposed in [19].A large number of dynamical systems such as manipulators, inverted pendulums, and so on [20, 21] have nonlinear models. By employing some techniques such as feedback linearization, the nonlinearities can be cancelled and one can deal...