yes. like dinoflagellata.

Dinoflagellata has two flagella, one equatorial and one longitudinal. It uses these two flagella to whirl around (which is what their name means. dino in dinoflagellata means to whirl).

Tamara Fedorovna Vozzhennikova has written:

'Fossil dinoflagellates from Jurassic, Cretaceous, and Paleogene deposits of the USSR' -- subject(s): Dinoflagellata, Fossil, Fossil Dinoflagellata, Paleobotany, Russia

Dinoflagellata and Pyrrophyta are two seperate Phylums, but share some of the same members. Pyrrophyta encompasses more organisms, and a working dichotomous key cannot have two phylum that share any of the same members; it defeats the point of seperating the organisms in the first place.

Noctiluca is a dinoflagellate in the Domain Eukaryota, Superphylum Alveolata, Phylum Dinoflagellata, in the class Noctiluciphyceae, and in the order Noctilucales.