  This paper presents a new theory of the dynamical tides of celestial bodies.
It is founded on a Newtonian creep instead of the classical delaying approach
of the standard viscoelastic theories and the results of the theory derive
mainly from the solution of a non-homogeneous ordinary differential equation.
Lags appear in the solution but as quantities determined from the solution of
the equation and are not arbitrary external quantities plugged in an elastic
model. The resulting lags of the tide components are increasing functions of
their frequencies (as in Darwin's theory), but not small quantities. The
amplitudes of the tide components depend on the viscosity of the body and on
their frequencies; they are not constants. The resulting stationary rotations
(pseudo-synchronous) have an excess velocity roughly proportional to
$6ne^2/(\chi^2+1/\chi^2)$ ($\chi$ is the mean-motion in units of one critical
frequency - the relaxation factor - inversely proportional to the viscosity)
instead of the exact $6ne^2$ of standard theories. The dissipation in the
pseudo-synchronous solution is inversely proportional to $(\chi+1/\chi)$. In
the inviscid limit it is roughly proportional to the frequency (as in standard
theories), but that behavior is inverted when the viscosity is high and the
tide frequency larger than the critical frequency. For free rotating bodies,
the dissipation is given by the same law, but now $\chi$ is the frequency of
the semi-diurnal tide in units of the critical frequency. This approach fails
to reproduce the actual tidal lags on Earth. In this case, to reconcile theory
and observations, we need to assume the existence of an elastic tide superposed
to the creeping tide. The theory is applied to several Solar System and
extrasolar bodies and currently available data are used to estimate the
relaxation factor $\gamma$ (i.e. the critical frequency) of these bodies.
