  We develop a general theory for two-dimensional (2D) anomalous Floquet
higher-order topological superconductors (AFHOTSC), which are dynamical
Majorana-carrying phases of matter with no static counterpart. Despite the
triviality of its bulk Floquet bands, an AFHOTSC generically features the
simultaneous presence of corner-localized Majorana modes at both zero and
$\pi/T$ quasi-energies, a phenomenon beyond the scope of any static topological
band theory. We show that the key to AFHOTSC is its unavoidable singular
behavior in the phase spectrum of the bulk time-evolution operator. By mapping
such evolution-phase singularities to the stroboscopic boundary signatures, we
classify all 2D AFHOTSCs that are protected by a rotation group symmetry in
symmetry class D. We further extract a higher-order topological index for
unambiguously predicting the presence of Floquet corner Majorana modes, which
we confirm numerically. Our theory serves as a milestone towards a dynamical
topological theory for Floquet superconducting systems.
