Planar and spherical elliptic motions had been introduced by Karger and Novak [A. Karger, J. Novak, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York, London, 1985]. Also, a dual spherical elliptic motion has been defined by Yapar [Z. Yapar, Spatial conchoidal and elliptic motions, Mechanism and Machine Theory 27 ( 1) ( 1992) 75-91]. In this paper, we de. ne the elliptic motion on a dual hyperbolic unit sphere e (H) over tilde (2)(0) in the dual Lorentzian space D-1(3) with dual signature (+, +, -) and carry the results to the Lorentzian line space IR13 by means of Study's mapping. (C) 2008 Elsevier Ltd. All rights reserved.