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The combination of several mass‐decreasing processes may critically affect the structure of open clusters (OCs), to the point that most dissolve into the field in a time‐scale shorter than ≈1 Gyr. Therefore, as is observed, old OCs should be sparse within the Galaxy. These mass‐decreasing processes can only be quantifiably examined given the derivation of the fundamental parameters, age, distance and mass, for a sample of old OCs. In this paper we focus on four candidate old star clusters, namely, LK 1, LK 10, FSR 1521 and FSR 1555. The first two clusters, discovered by Le Duigou &amp; Knödlseder, are projected towards the Cygnus association, whilst the remaining two have been detected in the fourth quadrant as cluster candidates from stellar overdensities by Froebrich, Scholz &amp; Raftery. To analyse the target clusters we construct near‐infrared colour–magnitude diagrams (CMDs) and derive stellar radial density profiles (RDPs). The CMDs are constructed using Two Micron All‐Sky Survey (2MASS)  J ,  H  and  K  s  bands, and the intrinsic morphologies of the target OCs within these diagrams are revealed by applying a field‐star decontamination algorithm. Fundamental parameters are estimated with Padova isochrones built for the 2MASS filters. We derive extinctions to the objects within the range  3.4 ≤ A   V  ≤ 8.9 , which makes them suitable for the near‐infrared analysis, ages within 1.0–2.0 Gyr, and distances from the Sun within 1.4–4.5 kpc. These distances, in conjunction with the positions in the sky, place the present four OCs close to the solar circle  (≲0.6 kpc) . For LK 10 our photometry reaches a depth ≈3 mag below the main‐sequence turn off, from which we derive a relatively steep mass function slope  (χ= 2.4 ± 0.4)  when compared to the Salpeter value  (χ= 1.35) . LK 10 is a rather massive old OC, with a mass within  1360 ≤ m  (M ⊙ ) ≤ 4400 , for stars in the observed magnitude range and the extrapolation to  0.08 M ⊙  , respectively. The mass estimated in the restricted magnitude range for the remaining, more distant OCs is within  260 ≤ m  (M ⊙ ) ≤ 380 . However, similarity with the CMD morphology and red clump of LK 10 suggests that they may be as massive as LK 10. The RDPs are well represented by a King‐like function, except LK 10, which has a central cusp suggesting post‐core collapse. Structurally, LK 1, FSR 1521 and FSR 1555 are similar to a sample of nearby OCs of comparable age.

Investigating the age and structure of the infrared old open clusters LK 1, LK 10, FSR 1521 and FSR 1555