We present the sub-millimeter spectra from 450 GHz to 1550 GHz of eleven nearby active galaxies observed with the SPIRE Fourier Transform Spectrometer (SPIRE/FTS) onboard Herschel. We detect CO transitions from J_up = 4 to 12, as well as the two [CI] fine structure lines at 492 and 809 GHz and the [NII] 461 GHz line. We used radiative transfer models to analyze the observed CO spectral line energy distributions (SLEDs). The FTS CO data were complemented with ground-based observations of the low-J CO lines. We found that the warm molecular gas traced by the mid-J CO transitions has similar physical conditions (n_H2 ~ 10^3.2 - 10^3.9 cm^-3 and T_kin ~ 300 - 800 K) in most of our galaxies. Furthermore, we found that this warm gas is likely producing the mid-IR rotational H2 emission. We could not determine the specific heating mechanism of the warm gas, however it is possibly related to the star-formation activity in these galaxies. Our modeling of the [CI] emission suggests that it is produced in cold (T_kin < 30 K) and dense (n_H2 > 10^3 cm^-3) molecular gas. Transitions of other molecules are often detected in our SPIRE/FTS spectra. The HF J=1-0 transition at 1232 GHz is detected in absorption in UGC05101 and in emission in NGC7130. In the latter, near-infrared pumping, chemical pumping, or collisional excitation with electrons are plausible excitation mechanisms likely related to the AGN of this galaxy. In some galaxies few H2O emission lines are present. Additionally, three OH+ lines at 909, 971, and 1033 GHz are identified in NGC7130.
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