The phrase "on end" is often used to describe an uninterrupted stretch of time or consecutive sequence of events. Some synonyms for "on end" include "continuously," "unceasingly," "incessantly," "endlessly," "perpetually," and "uninterruptedly." These words all convey the sense of something that goes on and on without pause or interruption. Other possible synonyms for "on end" might include "without interruption," "without break," or "without letup." As with any set of synonyms, the nuance and connotation of these words may differ slightly, so it is important to choose the best one for the context and intended meaning of the sentence.