This article investigates the consensus tracking problem for high-order stochastic pure-feedback nonlinear multiagent systems (MASs) with dead zones. It should be pointed out that each follower's virtual and actual control items are the power-exponential functions with positive odd numbers instead of linear items. Because of the structural characteristics of the followers' dynamics, a technique called adding a power integrator is used, which effectively overcomes the difficulties of states and dead zone with power-exponential functions. Furthermore, radial basis function neural networks are employed to estimate unknown nonlinear functions and solve the problem of algebraic loop caused by the pure-feedback structure of MASs. Meanwhile, the problems of "explosion of complexity" caused by repeated differentiations of the virtual controller are solved by using the tracking differentiators. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semiglobally uniformly ultimately bounded in probability, and the tracking errors can converge to a small neighborhood of the origin. Finally, simulation results are presented to verify the effectiveness of the proposed approach.