The Higman-Sims sporadic simple group denoted by HS was originally defined [9] as a rank 3 group of automorphisms of a regular graph on 100 points, with point stabilizer the Mathieu group M,,. The group was independently discovered by G. Higman as a doubly transitive permutation group of degree 176 [S]. In 1968, J. Conway discovered a new simple group of order 2 *’ .3’. 54. 72. 11 .13 .23 in which many of the sporadic simple groups are involved [2]. In particular the Higman-Sims group is obtainable as the pointwise stabilizer of a 2-dimensional sublattice of the Leech Lattice [2, 3, 61. The ordinary characters of the Higman-Sims group and those of its automorphism group were calculated by Frame [7], and those of its double cover by Rudvalis [ 141. In his Ph. D. thesis, J. Thackray found using computer calculations where necessary the p-modular characters of HS for p = 2, 3, 5, 7, and 11 [ 171. The p-modular characters for p = 3, 5, 7, and 11 were also found independently by J. F. Humphreys [lo]. The 7- and ll-modular characters of the double cover of the Higman-Sims group were found by R. Parker [ 121. The main purpose of this paper is to find the 3- and 5-modular charac- ters for the double covers of the Higman-Sims group and its auto- morphism group denoted by 2 . HS and 2 . HS : 2, respectively. We calculate the 3-modular characters for 2 . HS and 2 . HS:2 by using standard methods of calculating many projective characters and seeing how to split them as sums of projective indecomposables. These calculations were all done by hand. On the other hand to determine the 5-modular