In 1969, Kupa proved that there exists functions $f:\ell_2(\mathbb N)\to \mathbb R$ of class $C^\infty$ so that $f(C_f)=[0,1]$, where $C_f=\{x\in\ell_2:\, Df(x)=0\}$ is the set of critical points. This shows the failure of the classical Morse-Sard theorem in infnite dimensions. However, in 2004, Azagra and Cepedello proved that any continuous function $f:\ell_2(\mathbb N)\to \mathbb R$ can be uniformly approximated by $C^\infty$ functions without critical points. This type of result can be seen as an approximate version of the Morse-Sard theorem. \medskip Several authors have studied to what extend Azagra and Cepedello's result can be generalized to functions $f:E\to F$ where $E$ and $F$ are Banach spaces with $\text{dim}(E)=\infty$. In 2019, Azagra, Dobrowolski and myself considered the case of separable Banach spaces and showed the same type of result to be true in many situations. The main purpose of this talk is to discuss the nonseparable case, which has been treated much more recently. In particular, in this presentation we will show an approximate Morse-Sard type result for the case of continuous functions $f:\ell_2(\Gamma)\to \mathbb R$, where $\Gamma$ is an arbitrary infinite set. Moreover, similar results are also true for more general nonseparable Banach spaces $E$ and $F$. \medskip This is a joint work with Daniel Azagra and Mar Jim\'enez-Sevilla.