In 2004, Corteel and Lovejoy introduced the notion of overpartitions in order to give a combinatorial proof of several celebrated $q$-series identities. Let $\overline{p}(n)$ denote the number of overpartitions of $n$. Many scholars have been investigated subsequently congruence properties modulo powers of $2$ satisfied by $\overline{p}(n)$. Congruence properties modulo powers of 2 for $\overline{pp}(n)$ were also considered by several scholars, where $\overline{pp}(n)$ denotes the number of overpartition pairs of $n$. In this paper, utilizing some $q$-series identities and iterative computations, we prove several internal congruences and congruences modulo powers of 2 enjoyed by $\overline{p}(n)$ and $\overline{pp}(n)$. Moreover, we conjecture that these internal congruences and congruences are initial cases in the corresponding internal congruence families and congruence families. Finally, we pose a related conjecture and some questions that merit further investigation.

2004 年，Corteel 和 Lovejoy 引入了过度划分的概念，以便给出几个著名的组合证明$q$-系列身份。让$\stackrel{￣}{p}（n）$表示过度划分的数量$n$。随后许多学者研究了模幂的同余性质$2$满意于$\stackrel{￣}{p}（n）$。2 的模幂同余性质$\stackrel{￣}{pp}（n）$一些学者也考虑过，其中$\stackrel{￣}{pp}（n）$表示过度划分对的数量$n$。在本文中，利用一些$q$-级数恒等式和迭代计算，我们证明了几个内部同余和2的模幂同余$\stackrel{￣}{p}（n）$和$\stackrel{￣}{pp}（n）$。此外，我们推测这些内部同余和同余是相应的内部同余族和同余族中的初始情况。最后，我们提出了相关猜想和一些值得进一步研究的问题。