The asymptotic behavior of Jacobi polynomials $P_n^{\alpha + an,\beta + bn} (x)$ and Laguerre polynomials $L_n^{\alpha + an} (b + nx)$ is found when $n \to \infty $ and a, b, $\alpha $, $beta$ are real constants, $a > - 1$, $b > - 1$, and x is a real variable.