In human bimanual coordination an in-phase movement pattern is typically preferred to an anti-phase pattern. This preference results from a symmetry breaking in the dynamics between its components whose degree can be altered not only by variation of environmental but also intrinsic constraints. Recently, Carson et al. [Experimental Brain Research, 131, 196-214 (2000)] operationalized this notion and induced phase transitions from in-phase to anti-phase movement patterns. Here, we tackle this situation theoretically by introducing an additional parameter which represents the degree of symmetry into the HKB equation of bimanual coordination. We predict new phenomena to be observed experimentally when this parameter is manipulated independently or together with the movement rate, We derive the statistical properties of the extended system from a stochastic theory in detail and suggest how the predicted phenomena can be tested experimentally. (C) 2000 Elsevier Science B.V. All rights reserved.,