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Transverse spreading of a high-field domain in negative differential conductivity semiconductors has been analysed by a 2-dimensional computer simulation for various conditions. The results show that the transverse-spreading phenomena are very sensitive to the initial domain size in addition to the bias field, sample length and other parameters. During the domain spreading in the transverse direction, the domain growth rate is generally slower than that in the 1-dimensional case. In a long sample, or with a large initial domain size, the spreading velocity is very high, over 108 cm/s, while in a short sample, or with small domain size, an initial domain that is nucleated cannot spread and a local static domain is formed. Results of these computer simulations agree with the reported experiments and can also be qualitatively explained by a simple equivalent-circuit model.