ABSTRACT In this paper, we consider a viscoelastic Bresse-type system subjects to nonlinear damping, nonlinear time delay term, a finite memory and with homogeneous Dirichlet-Neumann-Neumann boundary conditions. Under a condition between the weight of delay term in the feedback and the weight of the term without delay, we prove, in case of equal speeds of wave propagation, new decay results that generalise and improve the recent results in the literature.