Open clusters older than ∼4Gyr are rare in the Galaxy. Affected by a series of mass-decreasing processes, the stellar content of most open clusters dissolves into the field on a time-scale shorter than ∼1Gyr. In this sense, improving the statistics of old objects may provide constraints for a better understanding of the dynamical dissolution of open clusters. Our main purpose is to investigate the nature of the globular cluster candidate FSR 1716, located at l=329.8° and b=-1.6°. We also derive parameters of the anti-centre open cluster Czernik 23 (FSR 834). Both objects have been detected as stellar overdensities in the Froebrich, Scholz & Raftery (2007MNRAS.374..399F
) star cluster candidate catalogue. The analyses are based on near-infrared colour-magnitude diagrams and stellar radial density profiles. The intrinsic colour-magnitude diagram morphology is enhanced by a field-star decontamination algorithm applied to the 2MASS J, H, and Ks
photometry. Isochrone fits indicate that FSR 1716 is more probably an old (∼7Gyr) and absorbed (AV
=6.3±0.2) open cluster, located ≃0.6kpc inside the solar circle in a contaminated central field. However, we cannot rule out the possibility of a low-mass, loose globular cluster. Czernik 23 is shown to be an almost absorption-free open cluster, ∼5 Gyrold, located about 2.5kpc towards the anti-centre. In both cases, solar and sub-solar ([Fe/H]~-0.5) metallicity isochrones represent equally well the stellar sequences. Both star clusters have a low mass content (≲200M☉
) presently stored in stars. Their relatively small core and cluster radii are comparable to those of other open clusters of similar age. These structural parameters are probably a consequence of the several Gyr of mass loss due to stellar evolution, tidal interactions with the disk (and bulge in the case of FSR 1716), and possibly giant molecular clouds. Czernik 23, and especially FSR 1716, are rare examples of extreme dynamical survivors. The identification of both as such represents an increase of ≃10% in the known population of open clusters older than ∼4Gyr in the Galaxy.