The finite generation and presentation of Schutzenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schutzenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite.2000 Mathematics subject classification: primary 20M05; secondary 20M18.