This paper proposes four approaches for approximately realizing nonlinear mappling of interval vectors by neural networks. In the proposed approaches, training data for the learning of neural networks are the paris of interval input vectors and interval target output vectors. The first approach is a direct application of the standard BP (Back-Propagation) algorithm with a pre-processed training data. The second approach is an application of the two BP algorithms. The third approach is an extension of the BP algorithm to the case of interval input-output data. The last approach is an extension of the third approach to neural network with interval weights and interval biases. These approaches are compared with one another by computer simulations.