Measurements of the jet activity in tt events produced in proton-proton collisions at √s = 8TeV are presented, using 20.3 fb-1 of data collected by the ATLAS experiment at the Large Hadron Collider. The events were selected in the dilepton eμ decay channel with two identi ed b-jets. The numbers of additional jets for various jet transverse momentum (pT) thresholds, and the normalised differential cross-sections as a function of pT for the ve highest-pT additional jets, were measured in the jet pseudorapidity range |η| < 4.5. The gap fraction, the fraction of events which do not contain an additional jet in a central rapidity region, was measured for several rapidity intervals as a function of the minimum pT of a single jet or the scalar sum of pT of all additional jets. These fractions were also measured in different intervals of the invariant mass of the eμbb system. All measurements were corrected for detector effects, and found to be mostly well-described by predictions from next-to-leading-order and leading-order tt event generators with appropriate parameter choices. The results can be used to further optimise the parameters used in such generators.