  In this contribution we present two new proposals for measuring the general
relativistic gravitomagnetic component of the gravitational field of the Earth.
One proposal consists of the measurement of the difference of the rates of the
perigee $\psi$ from the analysis of the laser--ranged data of two identical
Earth'artificial satellites placed in equal orbits with supplementary
inclinations. In this way the impact of the aliasing classical secular
precessions due to the even zonal harmonics of the geopotential would be
canceled out, although the non--gravitational perturbations, to which the
perigees of LAGEOS--type satellites are particularly sensitive, should be a
limiting factor in the obtainable accuracy. With a suitable choice of the
inclinations of the orbital planes it would be possible to reduce the periods
of such insidious perturbations so to use not too long observational time
spans. However, the use of a pair of drag--free satellites would greatly reduce
this problem, provided that the time span of the data analysis does not excess
the lifetime of the drag--free apparatus. In the other proposal the difference
of the rotational periods of two counter-revolving particles placed on a
friction-free plane in a vacuum chamber at the South Pole should be measured in
order to extract the relativistic gravitomagnetic signal. Among other very
challenging practical implications, the Earth's angular velocity
$\omega_{\oplus}$ should be known at a $10^{-15}$ rad s$^{-1}$ level from VLBI
and the friction force of the plane should be less than $2\times 10^{-9}$ dyne.
