In this paper we propose the Possibilistic C-Means in Feature Space and the One-Cluster Possibilistic C-Means in Feature Space algorithms which are kernel methods for clustering in feature space based on the possibilistic approach to clustering. The proposed algorithms retain the properties of the possibilistic clustering, working as density estimator in feature space and showing high robustness to outliers, and in addition are able to model densities in the data space in a non-parametric way. One-Cluster Possibilistic C-Means in Feature Space can be seen also as a generalization of One-Class SVM.