Partial periodicity search, i.e., search for partial periodic patterns in time-series databases, is an interesting data mining problem. Previous studies on periodicity search mainly consider finding full periodic patterns, where every point in time contributes (precisely or approximately) to the periodicity. However, partial periodicity is very common in practice since it is more likely that only some of the time episodes may exhibit periodic patterns.We present several algorithms for efficient mining of partial periodic patterns, by exploring some interesting properties related to partial periodicity, such as the Apriori property and the max-subpattern hit set property, and by shared mining of multiple periods. The max-subpattern hit set property is a vital new property which allows us to derive the counts of all frequent patterns from a relatively small subset of patterns existing in the time series. We show that mining partial periodicity needs only two scans over the time series database, even for mining multiple periods. The performance study shows our proposed methods are very efficient in mining long periodic patterns.