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We present Spitzer high-resolution spectra of off-nuclear regions in the central cluster galaxies NGC 1275 and NGC 4696 in the Perseus and Centaurus clusters, respectively. Both objects are surrounded by extensive optical emission-line filamentary nebulae, bright outer parts of which are the targets of our observations. The 10–37 μm spectra show strong pure-rotational lines from molecular hydrogen revealing a molecular component to the filaments which has an excitation temperature of ∼300−400 K. The flux in the 0−0 S(1) molecular hydrogen line correlates well with the strength of the optical lines, having about 3 per cent of the Hα+[N ii] emission. The 11.3-μm polycyclic aromatic hydrocarbon feature is seen in some spectra. Emission is also seen from both low- and high-ionization fine-structure lines. Molecular hydrogen cooler than ∼400 K dominates the mass of the outer filaments; the nebulae are predominantly molecular. [ABSTRACT FROM AUTHOR]