Methods and apparatus well suited for supporting communications over different ranges in, for example, a peer to peer wireless communications system, are described. In the peer to peer network at least some of the types of signals, e.g., peer discovery signals and/or paging signals, are transmitted with no closed loop power control. An exemplary peer to peer timing structure includes air link resources allocated for a particular type of signaling in which the resources are segmented into multiple blocks which do not overlap in time, different ones of the multiple blocks being associated with different ranges. The characteristics of the basic transmission units of the multiple blocks based on range are different, e.g., tone size and symbol width are different. A wireless communications device implements the peer to peer timing structure and uses resources from different range based blocks at different times. Data traffic transmission units may be the same regardless of the range.