In recent years a number of novel distributed parameter estimation algorithms have been developed stimulated by applications in cognitive radio, robotics, wireless networks and sensor networks. However, existing performance analyses have used white noise assumptions extensively. Here, we analyse for the first time a class of diffusion LMS strategies under autocorrelation assumptions. Further, we obtain a result in the white noise setting which provides a new understanding of existing steady state mean square error results. We treat the Adapt-then-Combine (ATC) algorithm.