Abstract This paper describes the asymptotic behavior of solutions of a class of semilinear ultrahyperbolic equations with variable coefficients. One consequence of the general analysis is a uniqueness theorem for a mixed boundary-value problem. Another demonstrates unique continuation at infinity. These results extend previous work by M. H. Protter, [Asymptotic decay for ultrahyperbolic operators, in “Contributions to Analysis” (Lars Ahlfors et al., Eds.), Academic Press, New York, 1974], and A. C. Murray and M. M. Protter, [ Indiana U. Math. J. 24 (1974) , 115–130], on a more restricted class of equations.