This paper discovers anomalies in activity networks under generalized precedence relations ( GPＲs) ，which arebeyond the explanations of current time parameters． For example，under the conditions of unchanged project completion time and other activity durations，an activity’s start time could be earlier than its earliest one，its finish time could be later than its latest one，and a prolongation of its duration could be greater than its total float． By researching the anomalies，new concepts of hidden times，hidden floats and false floats of activities are proposed to reveal hidden properties under GPＲs，and algorithms for them are designed．In many cases ( particularly adjusting activity durations) ，the hidden times，hidden floats and false floats instead of the current time parameters are perfectly suitable for practices． Furthermore，adjusting activity durations is an important measure for project scheduling，and as a common view，the allowable maximum prolongation of an activity’s duration is equal to the activity’s classic total float． However，our study tests that the view is wrong under GPＲs，and in this paper，an algorithm for the correct maximum prolongation of an activity’s duration is designed based on the hidden time parameters．