Conclusions. The counter-rotating outer halo implies a merger remnant, as does the increase in velocity dispersion at similar to 70 ''. From simulations it seems plausible that the merger that caused the increase in velocity dispersion was a spiral-spiral merger. Our Jeans models are completely consistent with a no dark matter scenario, however, some dark matter can be accommodated, although at much lower concentrations than predicted by ACDM simulations. This indicates that NGC 7507 may be a dark matter free elliptical galaxy. Regardless of whether NGC 7507 is completely dark matter free or very dark matter poor, it is at odds with predictions from current ACDM cosmological simulations. It may be possible that the observed velocity dispersions could be reproduced if the galaxy is significantly flattened along the line of sight (e.g. due to rotation); however, invoking this flattening is problematic.