Time overlapping of acoustic signals, which so often occurs in real life, is a challenge for current state-of-the-art sound recognition systems. In this work, we propose an approach for detecting, identifying and positioning a set of simultaneous acoustic events in a room environment, using multiple arbitrarily-located microphone arrays, and working in real time. Assuming a set of estimated acoustic source positions, the use of a frequency invariant nullsteering beamformer for each position and each array yields a set of signals which show different balances among the various acoustic sources. For each signal, a model-based likelihood computation is carried out to obtain a matrix of likelihood scores. Then a MAP criterion is used to jointly detect the event classes and assign each of them to a given source position. Experimental results with two sources, one of which is speech, and two threemicrophone linear arrays are reported, and a comparison with alternatives approaches is carried out.