Discriminative training is a powerful tool in acoustic modeling for automatic speech recognition. Its strength is based on the direct minimisation of the number of errors committed by the system at recognition time. This is usually accomplished by de ning an auxiliary function that characterises the behaviour of the system, and adjusting the parameters of the system in a way that this function is minimised. The main drawback of this approach is that a task speci c training database is needed. In this paper an alternative procedure is proposed: task adaptation using task independent databases. It consists in the combination of acoustic information|estimated using a general purpose training database|, and linguistic information|taken from the de nition of the task|. In the experiments carried out, this technique has led to great improvement in the recognition of two di erent tasks: clean speech digit strings in English and dates in Spanish over the telephone wire.