  In this contribution we aim to study the stability boundaries of solutions at
equilibria for a second-order oscillator networks with SN-symmetry, we look for
non-degenerate Hopf bifurcations as the time-delay between nodes increases. The
remarkably simple stability criterion for synchronous solutions which, in the
case of first-order self-oscillators, states that stability depends only on the
sign of the coupling function derivative, is extended to a generic coupling
function for second-order oscillators. As an application example, the stability
boundaries for a N-node Phase-Locked Loop network is analysed.
