In this paper, we define i1'1 e-curvature function, r"' (a,,...,ar ) -curvature çenter and (n~ r) -curvature hyperplane for the curve of Lorentzian space. We prove that the locus of centers of spheres that has p as the r-multiple contact point with curve is the (n - r) -curvature hyperplane in the n- dimensional Lorentzian space. We also consider some special cases. In the final section we çalculate the r'*(a,... ar ) -curvature centers Cr (t)(r = 2 or 3) of some special curves.