  Let $L$ be the operator defined on $C^2$ functions by $$L
f(x)=\int[f(x+h)-f(x)-1_{(|h|\leq 1)}\nabla f(x)\cdot
h]\frac{n(x,h)}{|h|^{d+\alpha(x)}}dh.$$ This is an operator of variable order
and the corresponding process is of pure jump type. We consider the martingale
problem associated with $L$. Sufficient conditions for existence and uniqueness
are given. Transition density estimates for $\alpha$-stable processes are also
obtained.
