This paper proposes a completely nonparametric method for estimating mixture cure models, focusing on the estimation of the incidence and latency functions. The proposed estimators are based on the Beran estimator of the conditional survival function and are shown to be local maximum likelihood estimators. An iid representation is derived for the nonparametric incidence estimator, leading to the development of an asymptotically optimal bandwidth. A bootstrap bandwidth selection method is also introduced. The performance of the nonparametric estimators is compared with existing semiparametric approaches through a simulation study, and the practical behavior of the bootstrap bandwidth selector is assessed. Finally, the method is applied to a dataset of colorectal cancer patients from the University Hospital of A Coruña (CHUAC). The results demonstrate the effectiveness of the nonparametric approach, particularly in scenarios where the semiparametric assumptions do not hold.This paper proposes a completely nonparametric method for estimating mixture cure models, focusing on the estimation of the incidence and latency functions. The proposed estimators are based on the Beran estimator of the conditional survival function and are shown to be local maximum likelihood estimators. An iid representation is derived for the nonparametric incidence estimator, leading to the development of an asymptotically optimal bandwidth. A bootstrap bandwidth selection method is also introduced. The performance of the nonparametric estimators is compared with existing semiparametric approaches through a simulation study, and the practical behavior of the bootstrap bandwidth selector is assessed. Finally, the method is applied to a dataset of colorectal cancer patients from the University Hospital of A Coruña (CHUAC). The results demonstrate the effectiveness of the nonparametric approach, particularly in scenarios where the semiparametric assumptions do not hold.