In the paper, the structure of spaces $\mathcal{D}'^{(M_\lambda)}_{L^\tau,\mu}(R)$ $(r\in[1,\infty),\ \mu\in R)$ of weighted ultradistributions of the Beurling type and the space $\mathcal S'^{(M_\alpha)}(R)$ of tempered ultradistribution of the Beurling type is investigated, as well as the dual spaces of the spaces of weighted ultradif-ferentiable functions and the space of rapidly decreasing ultradifferen-tiable functions, which are defined in [4], their relation with the known spaces of distributions and ultradistributions and the properties of the elementary operations in those spaces.