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The behaviour of the lengths of spectral gaps$\{\gamma_{n}(q)\}_{n=1}^{\infty}$ of the Hill-Schr\"odinger operators  S(q)u=-u''+q(x)u,\quad u\in \mathrm{Dom}(S(q)) with real-valued 1-periodicdistributional potentials $q(x)\in H_{1{-}per}^{-1}(\mathbb{R})$ is studied. Weshow that they exhibit the same behaviour as the Fourier coefficients$\{\widehat{q}(n)\}_{n=-\infty}^{\infty}$ of the potentials $q(x)$ with respectto the weighted sequence spaces $h^{s,\varphi}$, $s>-1$, $\varphi\in\mathrm{SV}$. The case $q(x)\in L_{1{-}per}^{2}(\mathbb{R})$, $s\in\mathbb{Z}_{+}$, $\varphi\equiv 1$ corresponds to the Marchenko-OstrovskiiTheorem.

Spectral gaps of the one-dimensional Schr\"odinger operators with singular periodic potentials