High damping and high stiffness (HDHS) viscoelastic materials, which exhibit desired energy-dissipating capability and structural integrity, may be achieved by using negative-stiffness inclusions, such as ferroelastic particles, in composite materials. However, stability has long been questioned for such composites to be realistic. Wang and Ko (pp. 2070–2079) examine a two-dimensional, two-phase, negative-stiffness viscoelastic composite under partial displacement loading by time–domain analysis with the finite element method. It was found that force responses may be stable or unstable, depending on the amount of negative stiffness. A small amount of negative stiffness in the viscoelastic composites may not deteriorate their stability, but is insufficient to trigger HDHS. Through examining the existing stability criteria of three-dimensional composites, the softening anomaly in the overall viscoelastic stiffness may be in the stability range, indicating stable damping enhancement. However, simultaneously enhancing damping and stiffness violates ellipticity requirements, hence the system is unstable/metastable. The cover image shows stress distributions around the inclusion of the two-dimensional composite in the background and stiffness/damping anomalies, as well as divergent force responses, deviating from expected sinusoidal responses.