The one-dimensional alternating antiferromagnet with H=2JΣnS⃗ 2n⋅S⃗2n−1+2J′ΣnS⃗2n⋅S⃗2n+1 is studied for J′≪J. For β−1≡kBT≪J the susceptibility is expanded in powers of the exciton density as χT∝ A (βJ′, J′/J)e−2βJ + B(βJ′,J′/J)e−4βJ+⋯ and the coefficients A and B are calculated for J′/J→0. The calculation of B(βJ′,0) required the evaluation of the two-exciton scattering matrix. The interactions between excitons which affect the susceptibility are found to be repulsive. As a result, the coefficient B is correctly predicted by the usual assumption that excitons obey localized statistics. A general discussion relating statistics to the on-shell forward-scattering t matrix enables one to understand the difference between the statistical properties of spin waves and excitons. For opposite-spin excitons an attractive bound state is found to exist for all values of total momentum. Perturbation theory in J′/J is used to calculate the single-exciton dispersion relation at zero temperature as E(k) = (2J+5J'3/32J2) − (J′+J'2/2J−5J'3/32J) cosk − (J'2/4J+J'3/8J2) cos2k − (J'3/8J2)cos3k.