Binary offset carrier (BOC) signal synchronization is based on the correlation between the received and locally generated BOC signals. Thus, the multiple side-peaks in BOC autocorrelation are one of the main error sources in synchronizing BOC signals. Recently, new correlation functions with no side-peak were proposed for sine and cosine phased BOC signal synchronization, respectively, by the authors [3]. In this paper, we propose new correlation functions with no side-peak for alternative BOC (AltBOC) and composite BOC (CBOC) signals by using the similar approach to the previous work.