  We consider fully nonlinear elliptic integro-differential operators with
kernels of variable orders, which generalize the integro-differential operators
of the fractional Laplacian type in \cite{CS}. Since the order of
differentiability of the kernel is not characterized by a single number, we use
the constant \begin{align*} C_\varphi = \left( \int_{\mathbb{R}^n} \frac{1-\cos
y_1}{\vert y \vert^n \varphi (\vert y \vert)} \, dy \right)^{-1} \end{align*}
instead of $2-\sigma$, where $\varphi$ satisfies a weak scaling condition. We
obtain the uniform Harnack inequality and H\"older estimates of viscosity
solutions to the nonlinear integro-differential equations.
