Process mining is an active research topic in the cross field of process management and data mining. In an actual business environment, the recorded data of a process execution that may be supported by different computer systems is scattered into different event log files. It is necessary to merge the scattered data into one single event log file when applying current process mining techniques and tools for process mining. This mission is still challenging, however, because of the complex relationships between cases in two logs and the possible lack of information for the merging. In this paper, event log merging for process mining is regard as a type of search and optimization problems based on the formal definition, and a merging approach with a hybrid artificial immune algorithm is presented in order to achieve the event log merging with many to many relationship between cases in the two event logs. In the merging approach, the clonal selection principle is selected as its underlying principle, which requires the matching process to undergo iterations of clonal selection, hypermutation and receptor editing in order to get the best solution. The algorithm starts from an initial population produced with a heuristic approach. Two factors, occurrence frequency and temporal relation, are designed in the affinity function to evaluate the individuals in the population. In addition, immunological memory and simulated annealing are exploited to make the artificial immune merging jumping out from the trap of local optima. Experimental results show that the hybrid algorithm has good performance in merging logs with complex cases relationships, and the heuristic approach for initial population can speed the process of the evolution. This paper also discusses the data distribution methods in which the log merging problems can be distributed.