The Calderón projector is a classical object in the study of boundary value problems for a (uniformly) elliptic operator $P$ on a compact manifold with boundary. If the order of $P$ is $m$ then the Calderón projector is a projection in the space of $m$-tuples of functions on the boundary to the subspace of Cauchy data of solutions $u$ of the equation $Pu=0$. An important result is that it is a pseudodifferential operator. We study the Calderón projector in the case where the boundary and operator have singularities of fibred cusp type and show that it is a phi-pseudodifferential operator. This is joint work with K. Fritzsch und E. Schrohe.