This paper introduces a new class of multivariable operators called $(n_1,\cdots ,n_m)$-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators $\mathcal{Q}=({\mathcal{Q}}_1,\cdots ,{\mathcal{Q}}_m)$ is said to be an $(n_1,\cdots ,n_m)$-hyponormal tuple for some $(n_1,\cdots ,n_m)\in {\mathbb{N}}^m$ if

$$\sum _{1\le k,l\le m}⟨[{\mathcal{Q}}_k^{\ast n_k},{\mathcal{Q}}_l^{n_l}]{\omega }_k\mid {\omega }_l⟩\ge 0,\mathrm{\forall }({\omega }_k{)}_{1\le k\le m}\in {\mathcal{K}}^m.$$

We show several properties of this class that correspond to the properties of joint hyponormal operators.