N-phosphonomethylamines are produced by reaction of an amine substrate with a halomethylphosphonic acid or salt thereof, a hydroxymethylphosphonic acid or salt thereof, or a dehydrated self-ester dimer, trimer or oligomer of hydroxymethylphosphonic acid. Among the products that may be prepared according to the process are N-phosphonomethylaminocarboxylic acids such as (e.g.) glyphosate, N-phosphonomethylaminoalkanols such as (e.g.) hydroxyethlaminomethylphosphonic acid, and N-acylaminomethylphosphonic acids such as (e.g.) N-carbamylaminomethylphosphonic acid. Certain reactions are conducted with a substantial excess of amine reactant in order to drive the conversion while avoiding excessive formation of bis(N-phosphonomethyl)amine by-products. Other reactions use a secondary amine substrate (such as iminodiacetic acid) and can be conducted at substantial equimolar ratios of halomethylaminomethylphosphonic acid or hydroxyaminomethylphosphonic acid to secondary amine reactant without significant formation of bis(phosphonomethyl)amine by-products. Further disclosed is a process for the preparation of hydroxymethylphosphonic acid self-ester dimers, trimers and oligomers by azeotropic dehydration.