  In this paper, we define constructive analogues of second-order set theories,
which we will call $\mathsf{IGB}$, $\mathsf{CGB}$, $\mathsf{IKM}$, and
$\mathsf{CKM}$. Each of them can be viewed as $\mathsf{IZF}$- and
$\mathsf{CZF}$-analogues of G\"odel-Bernays set theory $\mathsf{GB}$ and
Kelley-Morse set theory $\mathsf{KM}$. We also provide their proof-theoretic
strengths in terms of classical theories, and we especially prove that
$\mathsf{CKM}$ and full Second-Order Arithmetic have the same proof-theoretic
strength.
