  Fowler introduced the notion of a product system: a collection of Hilbert
bimodules $\mathbf{X}=\left\{\mathbf{X}_p:p\in P\right\}$ indexed by a
semigroup $P$, endowed with a multiplication implementing isomorphisms
$\mathbf{X}_p\otimes_A \mathbf{X}_q\cong \mathbf{X}_{pq}$. When $P$ is
quasi-lattice ordered, Fowler showed how to associate a $C^*$-algebra
$\mathcal{NT}_\mathbf{X}$ to $\mathbf{X}$, generated by a universal
representation satisfying some covariance condition. In this article we prove a
uniqueness theorem for these so called Nica-Toeplitz algebras.
