Summary: In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean \((n+1)\)-space \(\mathbb{E}^{n+1}\). Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces \(\mathbb{E}^{3}\) and \(\mathbb{E}^{4}\), respectively. We have also obtained some basic properties of generalized rotational surfaces in \(\mathbb{E}^{4}\) and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in \(\mathbb{E}^{3}\) and \(\mathbb{E}^{4}\), respectively.