The concept of neural network models (NNM) is a statistical strategy which can be used if a superposition of any forcing mechanisms leads to any effects and if a sufficient related observational data base is available. In comparison to multiple regression analysis (MRA), the main advantages are that NNM is an appropriate tool also in the case of non-linear cause-effect relations and that interactions of the forcing mechanisms are allowed. In comparison to more sophisticated methods like general circulation models (GCM), the main advantage is that details of the physical background like feedbacks can be unknown. Neural networks learn from observations which reflect feedbacks implicitly. The disadvantage, of course, is that the physical background is neglected. In addition, the results prove to be sensitively dependent from the network architecture like the number of hidden neurons or the initialisation of learning parameters. We used a supervised backpropagation network (BPN) with three neuron layers, an unsupervised Kohonen network (KHN) and a combination of both called counterpropagation network (CPN). These concepts are tested in respect to their ability to simulate the observed global as well as hemispheric mean surface air temperature annual variations 1874 - 1993 if parameter time series of the following forcing mechanisms are incorporated : equivalent CO2 concentrations, tropospheric sulfate aerosol concentrations (both anthropogenic), volcanism, solar activity, and ENSO (all natural). It arises that in this way up to 83% of the observed temperature variance can be explained, significantly more than by MRA. The implication of the North Atlantic Oscillation does not improve these results. On a global average, the greenhouse gas (GHG) signal so far is assessed to be 0.9 - 1.3 K (warming), the sulfate signal 0.2 - 0.4 K (cooling), results which are in close similarity to the GCM findings published in the recent IPCC Report. The related signals of the natural forcing mechanisms considered cover amplitudes of 0.1 - 0.3 K. Our best NNM estimate of the GHG doubling signal amounts to 2.1K, equilibrium, or 1.7 K, transient, respectively.