  Moir\'e structures in van der Waals heterostructures lead to emergent
phenomena including superconductivity in twisted bilayer graphene and optically
accessible strongly-correlated electron states in transition metal
dichalcogenide heterobilayers. Dual periodicity moir\'e structures (DPMS)
formed in layered structures with more than two layers have been shown to lead
to ferromagnetism and multiple secondary Dirac points in TBG. Whilst in
principle it is possible to obtain DPMS in bilayers there has not been clear
experimental evidence of this yet. In this paper we present signatures of DPMS
in a twisted MoSe$_2$/WSe$_2$ bilayer revealed by resonance Raman spectroscopy.
We observed zone-folded acoustic and optical phonon modes with a wavevector
twice of the moir\'e wavevector, evidence of a dual periodicity moir\'e
heterostructure. These results simultaneously open up opportunities for new
emergent phenomena and an optical method for characterising DPMS in a wide
range of van der Waals heterostructures.
