  Multi-peaked spectra of the primordial gravitational waves are considered as
a phenomenologically relevant source of information about the dynamics of
sequential phase transitions in the early Universe. In particular, such
signatures trace back to specific patterns of the first-order electroweak phase
transition in the early Universe occurring in multiple steps. Such phenomena
appear to be rather generic in multi-scalar extensions of the Standard Model.
In a particularly simple extension of the Higgs sector, we have identified and
studied the emergence of sequential long- and short-lasting transitions as well
as their fundamental role in generation of multi-peaked structures in the
primordial gravitational-wave spectrum. We discuss the potential detectability
of these signatures by the proposed gravitational-wave interferometers.
