When it comes to finding alternative words for the phrase "running after," there are many options to consider. Some of the most common synonyms include pursuing, chasing, following, stalking, and hounding. Other options might include tailing, shadowing, tracking, or dogging. Each of these terms can be used to describe the act of actively trying to catch up with or reach someone or something that is moving away from the speaker or pursuer. No matter which synonym you choose, it's important to understand the context of your sentence or phrase to ensure that the meaning is clear and effective.