In  the reflexive structures in the category of numeration were studied. It was shown that every numerated reflexive set forms a ``numeration model of $\lambda$-calculus''. In this short note we formalize the concept of numeration models of $\lambda$-calculus, and study several interesting subclasses. Even though the class of numeration models does not coincide with the class of numerated reflexive sets, we can show that the class of numeration models with ``$\lambda$-definability'' property is equivalent to the class of numerated reflexive sets with ``$\lambda$-representability'' property. Through this we observe relation between $\lambda$-definability and acceptability of numerations discussed in .
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