  We extend some results on almost Gorenstein affine monomial curves to the
nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of
a nearly Gorenstein monomial curve in $\mathbb{A}^4$ is at most $3$, answering
a question of Stamate in this particular case. Moreover, we prove that, if
$\mathcal C$ is a nearly Gorenstein affine monomial curve which is not
Gorenstein and $n_1, \dots, n_{\nu}$ are the minimal generators of the
associated numerical semigroup, the elements of $\{n_1, \dots, \widehat{n_i},
\dots, n_{\nu}\}$ are relatively coprime for every $i$.
