  We extend the classical Brunel-Sucheston definition of the spreading model by
introducing the $\mathcal{F}$-sequences $(x_s)_{s\in\mathcal{F}}$ in a Banach
space and the plegma families in $\mathcal{F}$ where $\mathcal{F}$ is a regular
thin family. The new concept yields a transfinite increasing hierarchy of
classes of spreading sequences. We explore the corresponding theory and we
present examples establishing this hierarchy and illustrating the limitation of
the theory.
