This document summarizes research into mining "partially-ordered sequential rules" (POSR) from multiple sequences to address limitations in existing sequential rule mining algorithms. The researchers propose the RuleGrowth algorithm to efficiently mine POSR, where the items in a rule's antecedent and consequent are unordered. An extension called TRuleGrowth accepts a sliding window constraint to find rules occurring within a maximum time frame. Experiments on four real-life datasets show RuleGrowth and TRuleGrowth have good performance and scalability compared to baselines. Applying a sliding window constraint reduced the number of rules discovered by orders of magnitude. POSR also provided higher prediction accuracy than regular sequential rules in a sequence prediction application.