We study the problem of continuous monitoring of top-k queries over multiple non-synchronized streams. Assuming a sliding window model, this general problem has been a well addressed research topic in recent years. Most approaches, however, assume synchronized streams where all attributes of an object are known simultaneously to the query processing engine. In many streaming scenarios though, different attributes of an item are reported in separate nonsynchronized streams which do not allow for exact score calculations. We present how the traditional notion of object dominance changes in this case such that the k dominance set still includes all and only those objects which have a chance of being among the top-k results in their life time. Based on this, we propose an exact algorithm which builds on generating multiple instances of the same object in a way that enables efficient object pruning. We show that even with object pruning the necessary storage for exact evaluation of top-k q...