Lattice dynamics, topological phonons, and drumheadlike phononic surface states in ternary hexagonal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>KCu</mml:mi> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> ( <mml:math xmln

Ternary potassium copper chalcogenides $\mathrm{KCu}X$ ($X=$ Se, Te) crystallizing in the hexagonal space group $P{6}_{3}/mmc$, are investigated for their topological phonon characteristics using ab initio techniques. The computed phonon dispersion relations exhibit multiple symmetry-enforced features, including high-degeneracy points and a nodal plane at the Brillouin zone boundary, consistent with the nonsymmorphic nature of the space group. Furthermore, a network of phononic nodal lines is identified, originating from the band crossings along high-symmetry paths and planes. These nodal lines are protected by crystalline symmetries such as mirror and rotational operations. To explore the topological consequences of these bulk features, we compute the surface phonon spectra, revealing the emergence of drumheadlike surface states that span the projections of the bulk nodal lines onto the surface Brillouin zone. These states indicate the nontrivial topological nature of the phonon bands. Our findings establish $\mathrm{KCu}X$ ($X=$ Se, Te) compounds as promising candidates for emergent topological phonon phases beyond the usual topology of the electronic structure.