In this paper we present recently obtained results from [14] concerning the complexity of LTL model checking of safe Elementary Object Nets (Eos) in a novel and more algorithmic oriented way. Object nets are Petri nets which have Petri nets as tokens – an approach known as thenets-within-nets paradigm. Object nets are called elementary if the net system has a twolevelled structure. Due to these two modelling levels object nets are very suited to modelthe mobility of e.g. active objects or agents. The well known p/t nets can be viewed as aspecial case ofEos. For p/t nets the concept of safeness means that there is at most one token on each place. Since object nets have nested markings there are different possibilities to generalise this idea for Eos. In this paper we concentrate on the variant ofEossafeness that guarantees the finiteness of state spaces and show that for safe Eos the LTL model checking problem is PSpace-complete.