The liquid centrifuge using a density-gradient method has certainly played an essential role in almost every advance in molecular and cellular biology. For the velocity-sedimentation method, when a rotor reaches its full speed, the density-gradient solution establishes its stable profile and particles of the sample begin to separate and to form their respective bands, and to sediment toward the wall of rotor. While particles move outward in bands, some of the bands separate into more bands during sedimentation and sometimes the separated bands overtake and cross each other depending on local properties such as density, dispersion coefficient, particle size, etc. Then each band starts to separate and to sediment outward until reaching its respective isopycnic zone. The locations where the separated bands cross each other or combine together may be termed bifurcation point(s) in density-gradient centrifugation. The method of Poincare's bifurcation analysis together with numerical simulation are used to analyze the effect of various local properties on bifurcation point(s). It is found that a major factor in having bifurcation(s) is the steepness of the density-gradient profile. The other properties are minor. (C) 1997 Elsevier Science B.V.