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The problem of fragment of space debris located at geostationary orbit disposal is studied. For this purpose, a special spacecraft debris collector is used. The main part of disposal operation – rendezvous transfer with fragment of space debris - is studied. Relative motion of a spacecraft debris collector about the fragment of space debris is considered in an orbital cylindrical reference frame. Secular and periodic components of relative motion are determined in an implicit form. Spacecraft debris collector motion control is carried out by its transversal acceleration from thrust switching. Radial thrust component is equal to zero. Boundary conditions for rendezvous transfer are formulated in terms of secular and periodic components of motion. The Motion control program for secular components contained two active areas and passive areas between them. Active areas duration were determined as functions of boundary conditions and passive area duration (free parameter). An analytical solution for the determined control program is formulated in an implicit form. Satisfaction of boundary conditions for periodic components is carried out by passive area duration and rendezvous start moment determination. Equations to determine these parameters are formulated. Numerical simulation is carried out. [ABSTRACT FROM AUTHOR]