In this paper, a new consensus problem is investigated which is group consensus. It contains such consensus problem as a special case that all agents in a network reach a consistent value asymptotically. Consider a dynamic multi-agent system with connected undirected or connected bipartite graph topology and delays, two novel consensus protocols are introduced to solve the group consensus problem. The convergence analysis is discussed and the sufficient condition for system group convergence is obtained based on the frequency-domain analysis and generalized Nyquist criterion, respectively. And we know that the condition of group convergence is only depended on system's time delay and the adjacent weight between the agents, meanwhile, delay can affect the dynamic characteristics of the system. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.