  In this work, we study some classes of rotational surfaces in the
pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in
2-dimensional planes. First, we determine all such surfaces in the Minkowski
4-space $\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and
second kind. Then, we obtain rotational surfaces in $\mathbb{E}^4_2$ with zero
mean curvature and having pointwise 1--type Gauss map of second kind.
