  In the present time we observe a growing number of publications where the,
so-called, flow equations are successfully used to diagonalize Hamiltonians by
means of an appropriate unitary transformation. Here we discuss and compare the
flow equations (FE) method (proposed in 1994) with the method of one step
continuous unitary transformations (OS CUT) (proposed in 1982). It is shown
that the FE method can be considered as a generalization of the OS CUT approach
to the case of parameter dependent generator. The OS CUT method gives linear
differential equations for the diagonalization procedure. In the FE method the
system of differential equations is nonlinear. Finally we discuss the
generalization of idea of continuous unitary transformations for the case of
quantum equations of motion (Heisenberg picture and density matrix).
