A perfect pseudomatching M in a graph G is a spanning subgraph of G whose components are isomorphic to the star K-1(,3) or to K-2. Perfect pseudomatchings interpolate between perfect matchings, in which all components are K-2, and perfect star packings, in which all components are stars K-1(,3). In this contribution we present some results on perfect pseudomatchings with small number of components in some classes of fullerene graphs. (C) 2022 Elsevier Inc. All rights reserved.