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A new algorithm is developed whereby the cloud Liquid Water Path (LWP) and the Total Precipitable Water (TPW) may be determined from SSM/I microwave radiometric data. An artificial Neural Network (NN) with a five-neuron single hidden layer with five neurons yields the best results. The NN algorithm for TPW and LWP is compared with log-linear regression algorithms developed on the same database. The results obtained on the simulated dataset are nearly twice as good with this new algorithm. In particular, this NN seems to be able to give a better fit for large values of LWP. Furthermore, in the case of TPW, a validation and comparison with conventional algorithms is presented, which is based on SSM/I measurements and collocated radiosonde observations (RAOBs). The main conclusion is that the NN algorithm is more regular than most of the other algorithms. Through this particular study, we try to elaborate a general methodology. The conclusions concern the variability of the database used to develop and test retrieval algorithms and the relevant parameters to characterize the performance of an algorithm. [ABSTRACT FROM AUTHOR]