Spatio-temporal co-occurrence patterns represent subsets of object-types that are often located together in space and time. The aim of the discovery of partial spatio-temporal co-occurrence patterns (PACOPs) is to find co-occurrences of the object-types that are partially present in the database. Discovering PACOPs is an important problem with many applications such as discovering interactions between animals in ecology, identifying tactics in battlefields and games, and identifying crime patterns in criminal databases. However, mining PACOPs is computationally very expensive because the interest measures are computationally complex, databases are larger due to the archival history, and the set of candidate patterns is exponential in the number of object-types. Previous studies on discovering spatio-temporal co-occurrence patterns do not take into account the presence period (i.e., lifetime) of the objects in the database. This paper defines the problem of mining PACOPs, proposes a new monotonic composite interest measure, and proposes novel PACOP mining algorithms. The experimental results show that the proposed algorithms are computationally more efficient than the na < ve alternatives.