  Recent observations support the view that the universe is described by a FLRW
model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w
\leq -1/3$ at the present epoch. There are several theoretical suggestions for
the cosmological $\Lambda$ component and for the particular form of the energy
transfer between this dark energy and matter. This gives a strong motive for a
systematic study of general properties of two-fluid FLRW models. We consider a
combination of one perfect fluid, which is quintessence with negative pressure
($p_Q = w\epsilon_Q$), and another perfect fluid, which is a mixture of
radiation and/or matter components with positive pressure ($p = \beta
\epsilon_m$), which define the associated one-fluid model ($p = \gamma
\epsilon$). We introduce a useful classification which contains 4 classes of
models defined by the presence or absence of energy transfer and by the
stationarity ($w = const.$ and $\beta = const.$) or/and non stationarity ($w$
or $\beta$ time dependent) of the equations of state. It is shown that, for
given $w$ and $\beta$, the energy transfer defines $\gamma$ and, therefore, the
total gravitating mass and dynamics of the model. We study important examples
of two-fluid FLRW models within the new classification. The behaviour of the
energy content, gravitating mass, pressure, and the energy transfer are given
as functions of the scale factor. We point out three characteristic scales,
$a_E$, $a_{\cal P}$ and $a_{\cal M}$, which separate periods of time in which
quintessence energy, pressure and gravitating mass dominate. Each sequence of
the scales defines one of 6 evolution types.
