Summary: The \(k\)-body embedded ensembles of random matrices originally defined by Mon and French are investigated as paradigmatic models of stochasticity in Fermionic many-body systems. In these ensembles, \(m\) Fermions in \(l\) degenerate single-particle states, interact via a random \(k\)-body interaction which obeys unitary or orthogonal symmetry. We focus attention on the spectral properties of these ensembles. We always take the limit \(l\rightarrow\infty\). For \(2k>m\), the spectral properties of the \(k\)-body embedded unitary and orthogonal ensembles coincide with those of the canonical Gaussian unitary and orthogonal random-matrix ensemble, respectively. For \(k\ll m\ll l\), the spectral fluctuations become Poissonian. The reason for this behavior is displayed by constructing limiting ensembles. The case of embedded Bosonic ensembles (\(m\) Bosons in \(l\) degenerate single-particle states interact via a random \(k\)-body interaction which obeys unitary or orthogonal symmetry) is also considered and compared with the case of Fermions.