In this article, the sequence spaces $f_0(N^t)$ and $f(N^t)$ are introduced as the domain of Nörlund mean in the spaces $f_0$ and $f$ of almost null and almost convergent sequences which are isomorphic to the spaces $f_0$ and $f$, respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces $f_0(N^t)$ and $f(N^t)$ are determined. Finally, the classes $(\alpha(N^t):\mu)$ and $(\mu:\lambda(N^t))$ of matrix transformations are characterized for given sequence spaces $\lambda$ and $\mu$ together with two Steinhaus type results.