This paper proposes a completely nonparametric method for estimating mixture cure models. The method involves nonparametric estimators for both the incidence (probability of being cured) and the latency (survival function of uncured patients). These 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 an asymptotically optimal bandwidth selection. A bootstrap bandwidth selection method is introduced to improve the performance of the nonparametric incidence estimator. The method is compared with existing semiparametric approaches in a simulation study, where the performance of the bootstrap bandwidth selector is assessed. The method is then applied to a real dataset of colorectal cancer patients from the University Hospital of A Coruña. The results show that the nonparametric estimators perform well in both simulated and real data scenarios, particularly when the incidence is not a logistic function and the latency does not fit a proportional hazards model. The bootstrap bandwidth selector is shown to be effective in selecting optimal bandwidths for the nonparametric estimators. The paper also provides theoretical properties of the nonparametric estimators, including their asymptotic normality and mean squared error. The results demonstrate that the nonparametric approach is a viable alternative to semiparametric methods in cure model estimation.This paper proposes a completely nonparametric method for estimating mixture cure models. The method involves nonparametric estimators for both the incidence (probability of being cured) and the latency (survival function of uncured patients). These 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 an asymptotically optimal bandwidth selection. A bootstrap bandwidth selection method is introduced to improve the performance of the nonparametric incidence estimator. The method is compared with existing semiparametric approaches in a simulation study, where the performance of the bootstrap bandwidth selector is assessed. The method is then applied to a real dataset of colorectal cancer patients from the University Hospital of A Coruña. The results show that the nonparametric estimators perform well in both simulated and real data scenarios, particularly when the incidence is not a logistic function and the latency does not fit a proportional hazards model. The bootstrap bandwidth selector is shown to be effective in selecting optimal bandwidths for the nonparametric estimators. The paper also provides theoretical properties of the nonparametric estimators, including their asymptotic normality and mean squared error. The results demonstrate that the nonparametric approach is a viable alternative to semiparametric methods in cure model estimation.