Context. Galaxy groups and clusters are formidable cosmological probes. They permit the studying of the environmental effects on galaxy formation. A reliable detection of galaxy groups is an open problem and is important for ongoing and future cosmological surveys. Aims. We propose a probabilistic galaxy group detection algorithm based on marked point processes with interactions. Methods. The pattern of galaxy groups in a catalogue is seen as a random set of interacting objects. The positions and the interactions of these objects are governed by a probability density. The parameters of the probability density were chosen using a priori knowledge. The estimator of the unknown cluster pattern is given by the configuration of objects maximising the proposed probability density. Adopting the Bayesian framework, the proposed probability density is maximised using a simulated annealing (SA) algorithm. At fixed temperature, the SA algorithm is a Monte Carlo sampler of the probability density. Hence, the method provides “for free” additional information such as the probabilities that a point or two points in the observation domain belong to the cluster pattern, respectively. These supplementary tools allow the construction of tests and techniques to validate and to refine the detection result. Results. To test the feasibility of the proposed methodology, we applied it to the well-studied 2MRS data set. Compared to previously published Friends-of-Friends (FoF) group finders, the proposed Bayesian group finder gives overall similar results. However for specific applications, like the reconstruction of the local Universe, the details of the grouping algorithms are important. Conclusions. The proposed Bayesian group finder is tested on a galaxy redshift survey, but more detailed analyses are needed to understand the actual capabilities of the algorithm regarding upcoming cosmological surveys. The presented mathematical framework permits adapting it easily for other data sets (in astronomy and in other fields of sciences). In cosmology, one promising application is the detection of galaxy groups in photometric galaxy redshift surveys, while taking into account the full photometric redshift posteriors.