The most important members of this group are the phosphoric acids, where each phosphorus atom bonded to four oxygen atoms, one of them through a double bond, arranged as the corners of a tetrahedron. Two or more of these  tetrahedra may be connected by shared single-bonded oxygens, forming linear or branched chains, cycles, or more complex structures. The single-bonded oxygen atoms that are not shared are completed with acidic hydrogen atoms. Their generic formula is HPO, where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure.
These acids, and their esters and salts ("phosphates") include some of the best-known and most important compounds of phosphorus.  
The simplest member of this class is:
* Phosphoric acid proper (also called orthophosphoric acid or monophosphoric acid),  (or ), a triprotic acid. It forms orthophosphate salt and esters, commonly called phosphates.
The smallest compounds of this class with two or more phosphorus atoms are called "oligophosphoric acids", and the larger ones, with linear –P–O– backbones, are "polyphosphoric acids"; with no definite separation between the two. Some of the most important members are:
* Pyrophosphoric acid,  (or –O–), with four acid hydrogens.  Forms pyrophosphates.
* Triphosphoric acid (or tripolyphosphoric acid),  (or –O––O–), with five acidic hydrogens.  Forms triphosphates or tripolyphosphates.
* Tetraphosphoric acid,  (or (–O–)–O–), with six acidic hydrogens.  Forms tetraphosphates.
The backbone may be branched, as in:
* Triphosphono phosphoric acid,  or P(O)(–), a branched isomer of tetrapolyphosphoric acid.
The  tetrahedra may be connected to form closed –P–O– chains, as in:
* Trimetaphosphoric acid (or cyclotriphosphoric acid),  (or , (–P(O)(OH)–O–)), a cyclic molecule with three acidic hydrogens. Forms the trimetaphosphate salts and esters.
Metaphosphoric acid is a general term for phosphoric acids with a single cycle, (–P(O)(OH)–O–), whose elemental formula is .
Another compound that may be included in this class is
* Peroxomonophosphoric acid, HPO (or OP(OH)(OOH)), which can be seen as monophosphoric acid with a peroxide group replacing the oxygen atom in one of the hydroxyl groups