The spectrum of the two-particle spin-singlet (DeltaS(z) = 0, +/-1) excitat
ions of a weakly coupled antiferromagnetic spin-1/2 alternating (J(1) +/- d
elta) chain is calculated using a mean-field approximation for the intercha
in exchange (J(2)) by the quantum Monte Carlo method. The bandwidth change
of these excitations, the mass gaps in the singlet-singlet excitation spect
rum, the top boundaries of the bands and the velocities of these excitation
s are estimated as functions of the alternating bond delta. The temperature
s at which the singlet gaps close are determined.