Crosby (1974) adopted the Philibert-Dixon Principle:

“In constructing a classification of the mosses, primary weight must be given to characters of the sporophyte, and particularly the peristome; mosses with similar gametophytes but different peristomes must not  be grouped together but with mosses which have similar peristomes”

According to this principle Crosby thought that his classification would reflect phylogeny.

He observed that two kinds of peristomes occur in the Hookeriales:

1. The Daltoniaceous type:

• Papillose exostome.
• Inner plates narrower than outer ones.
• Segments of endostome papillose, basal membrane low or absent, no cilia
• Exothecial cells rectangular-subquadrate, evenly thickened.
• Seta often papillose.
• Calyptra laciniate at base, often hairy.

2. The Hookeriaceous type:

• Outer plates of exostome cross-striate with furrowed or zig-zag median line.
• Endostome finely papillose, high basal membrane, keeled segments, cilia usually absent.

Crosby (1974) arranged the Hookeriales in two main families according to the type of peristom.