Self-replication plays a central role in the origin of life and in strategies to synthesize life de novo. Studies on self-replication have focused mostly on isolated systems, while the dynamics of systems containing multiple replicators have received comparatively little attention. Yet most evolutionary scenarios involve the interplay between different replicators. Here we report the emergence of parasitic behavior in a system containing self-replicators derived from two subtly different building blocks 1 and 2. Replicators from 2 form readily through cross-catalysis by pre-existing replicators made from 1. Once formed, the new replicators consume the original replicators to which they owe their existence. These results resemble parasitic and predatory behavior that is normally associated with living systems and show how such lifelike behavior has its roots in relatively simple systems of self-replicating molecules.