We study the effect of soft gluon emission in the hadroproduction of squark-antisquark and gluino-gluino pairs at the next-to-leading logarithmic (NLL) accuracy within the framework of the minimal supersymmetric model. The one-loop soft anomalous dimension matrices controlling the color evolution of the underlying hard-scattering processes are calculated. We present the resummed total cross sections and show numerical results for proton-proton collisions at 14 TeV. For the gluino-pair production, the theoretical uncertainty due to scale variation is reduced to the few-percent level.