Abstract: Efforts geared at repositioning the international system to ensure peaceful coexistence among states have greatly been undermined by terrorist activities across the globe. Thus, while commerce and technology have brought the planet together in ways unimaginable, advances in communication, transportation and weaponry by nations now give room for unavoidable avenue for terrorist exploitation. This paper examined the impact of international terrorism in the international system. The paper utilized data drawn from the secondary sources which were analyzed within the context of Frustration/Aggression theory. The article revealed that frustration on the part of the terrorists about their perceived plights especially the United States support for Israel against the Palestinians is responsible for the prolonged terrorist attacks against the United States of America and Israel. Similarly, the article also found out that military interventionist foreign policies by the major powers aggravate and intensify terrorist attacks across the globe. Consequently, the article recommended among others, that Palestinians should be provided with some reliefs from their current stateless condition; efforts should be intensified in improving living conditions in less prosperous countries by providing disadvantaged people with employment and other opportunities for a better life as this will help to deter some potential terrorists.