Multi-level selection has proven to be an affective mean to provide resistance against parasites for catalytic networks (Cronhjort and Blomberg, 1997). One way to implement these multi-level systems is to group molecules into several distinct compartments (cells) which are capable of cellular division (where an offspring cell replaces another cell). In such systems parasitized cells decay and are ultimately displaced by neighboring healthy cells. However in relatively small cellular populations, it is also possible that infected cells may rapidly spread parasites throughout the entire cellular population. In which case, group selection may fail to provide resistance to parasites. In this paper, we propose a concurrent artificial chemistry (AC) which has been implemented on a cluster of computers where each cell is running on a single CPU. This multi-level selectional artificial chemistry called the Molecular Classifier Systems was based on the Holland broadcast language. An attribute inherent to such a concurrent system is that the computational complexity of the molecular species contained in a reactor may now affect the fitness of the cell. This molecular computational cost may be regarded as the chemical activation energy necessary for a reaction to occur. Such a property is often not considered in typical Artificial Life models. Our experimental results obtained with this system suggest that this activation energy property may improve the resistance to parasites for catalytic networks. This work highlights some of the benefits that could be obtained using a concurrent architecture on top of computational efficiency. We first briefly present the Molecular Classifier Systems, this is then followed by a description of the multi-level concurrent model. Finally we discuss the benefits of using this multi-level concurrent model to enhance evolutionary stability for catalytic networks in our AC.