Identify the error in the following sentence: After the policeman had ran for several miles, he finally caught up with the man who had stolen the purse.

The phrase "had ran" contains a grammatical error because it incorrectly uses the past participle form of the verb "to run." In English, the correct past participle is "run," not "ran." The structure "had" followed by a past participle is used to form the past perfect tense, which describes an action that was completed before another action took place. Therefore, the correct phrasing should be "had run." This maintains proper verb form and agrees with standard usage in English.

The other parts of the sentence are grammatically correct, with "finally" appropriately indicating the temporal sequence of events, "up with" correctly forming the phrasal verb for catching someone, and "several" accurately modifying "miles." This highlights that "had ran" is the only issue requiring correction.