The authors prove the existence of integral solutions for a functional differential inclusion of the form \(y'(t)\in Ay(t)+F(t,y_t)\), a.e. for \(t\in [\,0,b\,]\) subjected to the nonlocal condition \(y(t)+(\xi(y_{t_1},\dots,y_{t_p}))(t)=\phi(t)\), for \(t\in [\,-r,0\,]\), where \(A\) is a closed linear operator generating an integrated semigroup in a Banach space \(E\), \(F:[\,0,b\,]\times C([\,-r,0\,];E)\to 2^E\) is a bounded, closed, convex valued map, \(0