Let \(n\) be a positive integer. A function \(f\) is called \(n\)-analytic on an open set \(G\) in the complex plane if \(f\in C^n(G)\) and \(\bar{\partial}^nf=0\) in \(G\). Such a function has a unique representation \[ f(z)=f_0(z)+\bar{z}f_1(z)+\dots +\bar{z}^{n-1}f_{n-1}(z), \] where \(f_0,f_1,\dots f_{n-1}\) are holomorphic functions on \(G\). The authors provide necessary and/or sufficient conditions on a closed set \(F\) for any function \(f\) continuous on \(F\) and \(n\)-analytic in the interior of \(F\), to be the uniform limit on \(F\) of a sequence of \(n\)-analytic entire or meromorphic functions. The proofs involve the notions of Carathéodory and Nevanlinna domains, and the classical approximation theorems (Mergelyan, Arakelyan etc).