  We provide posterior contraction rates for constrained deep Gaussian
processes in non-parametric density estimation and classication. The
constraints are in the form of bounds on the values and on the derivatives of
the Gaussian processes in the layers of the composition structure. The
contraction rates are rst given in a general framework, in terms of a new
concentration function that we introduce and that takes the constraints into
account. Then, the general framework is applied to integrated Brownian motions,
Riemann-Liouville processes, and Mat{\'e}rn processes and to standard
smoothness classes of functions. In each of these examples, we can recover
known minimax rates.
