  We study the construction of nonuniform tight wavelet frames for the Lebesgue
space $L^2(\mathbb{R})$, where the related translation set is not necessary a
group. The main purpose of this paper is to prove the unitary extension
principle (UEP) and the oblique extension principle (OEP) for construction of
multi-generated nonuniform tight wavelet frames for $L^2(\mathbb{R})$. Some
examples are also given to illustrate the results.
