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In this article, we study the full theta lifting for two cases of type IIreductive dual pairs over a nonarchimedean local field. Firstly, we determinethe structure of the full theta lifts of all irreducible representations fordual pair $(\mathrm{GL}(2),\mathrm{GL}(2))$. Secondly, we prove that the fulltheta lift of an irreducible tempered representation is irreducible andtempered for dual pair $(\mathrm{GL}(n),\mathrm{GL}(n+1))$, where $n$ is apositive integer.

Full theta lifting for type II reductive dual pairs