Co-evolution of systems is the important process of systems mutual evolution, which allows forming the systems of higher hierarchical level.

Systems co-evolution arises when evolution of one system begins to impact on evolution of another system via interaction, i.e. when one system begins to adjust to the changes of another system (and vice versa) via the mechanism of adaptation, and this forms common speed of their evolution and common moments of intensification.

The process of co-evolution plays the role of positive feedback because of concurrence and simultaneity of participating systems. This makes the process of each system evolution many times faster, and concurrence of their functioning (co-operation) and mutual influence create the basis of the new system, which contain all the systems under co-evolution.

However, the process of co-evolution exists not in all situations between interacting systems. It ends in the situations as follow:
if the tie between systems becomes too rigid, i.e. mutual influence becomes functional. So, the systems lose independency and freedom of choice, then process of their evolution ends and they become the functional subsystems of one system;
if the power and intensity of systems interaction become lower of some threshold limit value, and this reduce mutual influence of systems to such level, where the processes of their evolution stop correlate;
if one system increases or decreases dramatically the rate of influence on another system. In this case the more powerful system actually subordinates functioning and evolution of less powerful system. The co-evolution process between systems may be renewed if their mutual influence will become commensurable.

Co-evolution may arise on different levels of systems organization:
Elements;
Elements and subsystems;
Subsystems;
Subsystems and entire system;
System and environment.
If interacting systems are of the same power of mutual influence, then the acceleration of evolution speed will be identical for each system. If interacting systems are of different power of mutual influence, then the speed of evolution of less powerful system will be higher in proportion to power of more powerful system. Under power of the system we understand the degree of maturity, availability of resources for existence and influence capabilities.

So, co-evolution of systems exists not in all situations, but only in specific conditions:
timeliness (regularity) and topological correctness of systems interaction;
sufficient level of interacting systems autonomy;
concurrence of systems powers.

The result of co-evolution is the system of higher hierarchical level, the evolution speed of such system is higher than the evolution speed of any system which is included into it.

The system of higher hierarchical level creates favorable conditions and contributes to more prolonged survival of systems under co-evolution, and this is the goal of co-evolution of complex systems.