  We use general L\"owner theory to define general slit L\"owner chains in the
unit disk, which in the stochastic case lead to slit holomorphic stochastic
flows. Radial, chordal and dipolar SLE are classical examples of such flows.
Our approach, however, allows to construct new processes of SLE type that
possess conformal invariance and the domain Markov property.The local behavior
of these processes is similar to that of the classical SLE.
