The combination synchronization (CS) and combination-combination synchronization (CCS) for
chaotic and hyperchaotic dynamical systems with the same dimensions are introduced and studied in
the literature. In this paper, we introduce the definition of CS and CCS for those systems with different
dimensions.Westate two schemes to achieve these kinds of synchronization based on the active
control technique. Two theorems are stated and proved to provide us with analytical expressions for
the control functions.Westate four hyperchaotic dynamical systems with different dimensions which
are used as examples to achieve CS and CCS. These examples are hyperchaotic detuned laser, Lorenz,
van der Pol and dynamos systems. These systems appeared in many important applications in applied
science, e.g., a ring laser system of two-level atoms, vacuum tube circuit and two coupled dynamos
system. The validity of the analytical control functions are tested numerically and good agreement is
found between them. The numerical solutions ofODEsystems are calculated by using the method of
Runge-Kutta of order 4. Other systems can be similarly studied