  We prove relative Fatou's theorem for nonnegative harmonic functions with
respect to a large class of killed subordinate Brownian motions with Gaussian
components in bounded $C^{1,1}$ open sets in $\mathbb{R}^{d}$, $d\geq 2$, which
asserts the existence of nontangential limit of the ratio of two harmonic
functions with respect to the killed processes. When $D=B(x_{0},r)$ is a ball
we prove Fatou theorem. That is, we establish the existence of nontangential
limit of a single nonnegative harmonic function. We also prove this is the best
result possible by showing that there is a nonnegative harmonic function which
does not have a tangential limit a.e. when $d=2$ and $D=B(0,1)$.
