  In the present study we consider the generalized rotational surfaces in
Euclidean spaces. Firstly, we consider generalized spherical curves in
Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of
generalized spherical surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $%
\mathbb{E}^{4}$ respectively. We have shown that the generalized spherical
surfaces of first kind in $\mathbb{E}^{4}$ are known as rotational surfaces,
and the second kind generalized spherical surfaces are known as meridian
surfaces in $\mathbb{E}^{4}$. We have also calculated the Gaussian, normal and
mean curvatures of these kind of surfaces. Finally, we give some examples.
