We introduce a new type of topological magnon matter: the magnonic pendant to electronic nodal-line semimetals. Magnon spectra of anisotropic pyrochlore ferromagnets feature twofold degeneracies of magnon bands along a closed loop in reciprocal space. These magnon nodal lines are topologically protected by the coexistence of inversion and time-reversal symmetry; they require the absence of spin-orbit interaction (no Dzyaloshinskii-Moriya interaction). We calculate the topological invariants of the nodal lines and show that details of the associated magnon drumhead surface states depend strongly on the termination of the surface. Magnon nodal-line semimetals complete the family of topological magnons in three-dimensional ferromagnetic materials.Introduction. Over the recent years, nontrivial topologies of magnon spectra have become a thriving field of research. In striking analogy to electronic topological matter [1], topological magnon matter has been identified. The 'drosophilae' of such topological magnon insulators (TMIs) [2], which are the pendant to electronic Chern insulators, are (twodimensional) ferromagnets on a kagome lattice with Dzyaloshinskii-Moriya interaction (DMI) [3][4][5][6][7][8][9][10]. The latter causes complex hopping matrix elements in the free-boson Hamiltonian of magnons and, thus, breaks time-reversal symmetry; this points towards the textured magnetic flux in the Haldane model [11]. As a result, Berry curvatures and Chern numbers are nonzero and cause topologically protected edge magnons. The latter revolve unidirectionally the sample in accordance with the bulk-boundary correspondence [12,13]. Recently, Cu-(1,3-benzenedicarboxylate) was identified as a TMI which is very well approximated by the kagome model [14]; TMIs on the honeycomb lattice have been proposed as well [15].The quest for topologically nontrivial systems has been initiated by the discovery of the magnon Hall effect [16,17] in ferromagnetic pyrochlore oxides, mostly because the transverse thermal Hall conductivity has been related to the Berry curvature of the bulk magnons [5,18,19]. The quite natural extension of the topological classification to three-dimensional systems lead to the discovery of magnon Weyl semimetals [20,21], in which the crossing points of two magnon bands act as source and sink of Berry flux (again, in close analogy to electronic systems [22, 23]).In this Letter, we complete the family of topological magnonic objects in three-dimensional ferromagnetic materials by predicting 'magnon nodal-line semimetals' (magnon NLSMs), the magnon pendant of electronic NLSMs [24][25][26][27][28][29]. For this purpose, we consider a ferromagnetic pyrochlore lattice with anisotropic exchange interactions but without spinorbit interaction (SOI). We find two nodal lines, that is, two closed loops in reciprocal space along which two magnon bands are degenerate. On top of this, we identify the protecting symmetries and calculate topological invariants of the nodal lines. Magnon spectra for the (111) surface feature drum...