In this paper, a theory of the causes of condensations i the central parts of open star clusters is developed, which are in the state of approximate statistical equilibrium. A method is proposed of establishing the mean diameter of star clusters. Owing to galactic rtation, clusters of central densities smaller than 4.5 solar masses/parsec^3 show some elongation in the direction of the galactic plane. Clusters of central densities larger than 0.5 solar masses/parsec^3 may, as a whole, be regarded as stationary and their state as statistically in equilibrium. Assuming Maxwell´s velocity distribution, stars from the central parts of the star clusters will, on account of the shorter relaxation time, tend to escape quicker than these from the border. The star clusters will therefore contract quicker around the centre than at the border. After the state of the cluster has become stationary its central part has a larger kinetic energy than the border parts, in spite of the fact that the star energies of various cluster regions adjust themselves. The paper derives a method of determining initial residual star velocities in the cluster. Today´s value of the residual velocity, together with the initial velocity, allow us to estimate the age of the star cluster. The theoretical results were applied to moving cluster Hyades. The age was estimated as 1.1 x 10^9 years. The theoretical flatness of the cluster 0.69 agrees well with the observed value of 0.07, given by van Bueren [19].
Structural peculiarities of most open star clusters have been studied. They could indicate dynamical influences and disruption of clusters. The distribution of the number of disturbed clusters relatively to the total number of clusters seems to suggest some connection with the distribution of the interstellar matter in the sky.
The data of 11 open star cluster complexes are presented. From the analysis of these data a conclusion is made of a probable existence of a rotating system of the star complexes.
In the seventies, astronomers from some European socialist countries, participating in the multilateral cooperation of the academies of these states, decided to collaborate in the detailed astrometric, photometric and spectrometri investigation of open star clusters. Hungarian scientists were expected to carry out tthe multicolour photometry of cluster member stars (at least to a certain extent). Considering that the majority of the programme stars are far too dim to be measured by the moderate-sized photoelectric telescopes of the Hungarian Academy of Sciences and that incividual photoelectric photometry of cluster members would be extremely time-consuming, photographic UBV photometry was chosen as the most advantageous solution. The first steps in this task have been taken - more than 200 plates were collected in these spectral bands - and a short review is presented on the observations in order to inform out cooperating partners. At the same time, a proposal is made with a view to supplementing the list of jointly studied open clusters and information is requested from our collaborators on cluster membership probabilities and spectre of stars in order to take the preliminary steps in laboratory measurements.