The actinophryids, Actinophrys and Actinosphaerium, exist only in a heliozoan form with no flagellum and with more elaborate bundles of microtubules supporting their axopods.

Some authors classified pedinellids within the order Ochromonadales, together with a variety of unrelated heterokonts such as Synuraceae and Bicosoecaceae, as part of the class Chrysophyceae or golden algae.

[6] The same year, John J. Lee and coauthors segregated the phagotrophic (i.e. without chloroplasts) pedinellids as a different order Ciliophryida under the polyphyletic class Heliozoea.

Other authors, such as Thomas Cavalier-Smith, went a step further and proposed treating pedinellids as a separate class, under the name of Pedinellea (spelt Pedinellophyceae under botanical nomenclature).

[8] Simultaneously, Cavalier-Smith proposed a slightly different classification where he created a new class Actinochrysea to embrace these three groups, avoiding the usage of Dictyochophyceae as a name.

[2] The next year, Cavalier-Smith and Ema E. Chao recognized that the chloroplast losses were polyphyletic, and the family Actinomonadaceae was transferred to Pedinellales on the basis of a molecular phylogenetic analysis.

[10] In 2018, he finally recognized class Dictyochophyceae, and created the subclass Pedinellia or Pedinellophycidae (equivalent to his earlier Actinochrysea/Actinochrysia) to lump together pedinellids and silicoflagellates.

Instead, Moestrup's 1995 classification is more commonly supported, where pedinellids are all contained in the order Pedinellales, rendering Ciliophryales a junior synonym.