This paper addresses the distributed average tracking (DAT) problem for a group of agents to track the average of multiple time-varying reference signals, each of which is available to only one agent, under local interaction with neighbors and an undirected graph. We consider three cases: 1) DAT for single-integrator dynamics with a chain of integrators in algorithm design; 2) DAT with swarm behavior for single-integrator dynamics; and 3) DAT with swarm behavior for double-integrator dynamics. First, a continuous distributed algorithm with a chain of two integrators is proposed for single-integrator dynamics, where each agent needs its own and its neighbors' filter outputs obtained through communication besides its absolute position, local relative positions, reference signal, and reference velocity. The introduced algorithm can deal with a wide class of reference signals with steady deviations among reference velocities. Then, two swarm-based DAT algorithms for, respectively, single- and double-integrator dynamics are presented. In the first swarm-based algorithm for single-integrator dynamics, each agent needs to measure the relative positions between itself and its neighbors, while in the second swarm-based algorithm for double-integrator dynamics, relative velocity information is required too. In both cases, the information can be obtained through local sensing. If correct initialization constraints can be achieved, the center of the agents will track the average of the reference signals and the agents will maintain connectivity and avoid interagent collision. Numerical simulations are also presented to illustrate the theoretical results. Finally, the algorithms presented in this paper are experimentally implemented and validated on a multirobot platform.