  We define partial product systems over N. They generalise product systems
over N and Fell bundles over Z. We define Toeplitz C*-algebras and relative
Cuntz-Pimsner algebras for them and show that the section C*-algebra of a Fell
bundle over Z is a relative Cuntz-Pimsner algebra. We describe the
gauge-invariant ideals in the Toeplitz C*-algebra.
