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The density of complex eigenvalues of random asymmetric $N\times N$ matricesis found in the large-$N$ limit. The matrices are of the form $H_0+A$ where $A$is a matrix of $N^2$ independent, identically distributed random variables withzero mean and variance $N^{-1}v^2$. The limiting density $\rho (z,z^*)$ isbounded. The area of the support of $\rho (z,z^*)$ cannot be less than $\piv^2$. In the case of $H_0$ commuting with its conjugate, $\rho (z,z^*)$ isexpressed in terms of the eigenvalue distribution of the non-perturbed part$H_0$.Comment: 10 pages, LaTeX2e, 1 eps figur

Large-Neigenvalue distribution of randomly perturbed asymmetric matrices