Nonmembranous structures found in eukaryotic cells include ribosomes, the cytoskeleton and centrioles.

Eukaryote ribosomes are similar in structure and function to those found in prokaryotes, but are larger, composed of small (40S) and large (60S) subunits that, when combined, have a size of 80S.

The eukaryote cytoskeleton functions in mainatining cell shape, movement of organelles in the cytoplasm (cyclosis), endo- and exocytosis.
 

                            Structure of eukaryote cytoskeleton filaments.

                                            Stained cytoskeleton of a eukaryote cell.
 
 

Centrioles are found in animal and some fungal cells, lying at right angles to one another near the nucleus in a region called the centrosome.  They are composed of nine triplets of microtubules arranged in a 9+0 arrangement and function in mitosis, flagella and cilia formation.