Measurements of the jet activity in $$ t\overline{t} $$ events produced in proton-proton collisions at $$ \sqrt{s}=8 $$ TeV 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 identified b-jets. The numbers of additional jets for various jet transverse momentum (p T) thresholds, and the normalised differential cross-sections as a function of p T for the five highest-p T additional jets, were measured in the jet pseudo-rapidity 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 p T of a single jet or the scalar sum of p T of all additional jets. These fractions were also measured in different intervals of the invariant mass of the $$ e\mu b\overline{b} $$ 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 $$ t\overline{t} $$ event generators with appropriate parameter choices. The results can be used to further optimise the parameters used in such generators.