  We discuss the possible existence of new long-range forces mediated by spin-1
or spin-0 particles. By adding their effects to those of gravity, they could
lead to apparent violations of the Equivalence Principle. While the vector part
in the couplings of a new spin-1 U boson involves, in general, a combination of
the B and L currents, there may also be, in addition, an axial part as well. If
the new force has a finite range \lambda, its intensity is proportional to
1/(\lambda^2 F^2), F being the extra U(1) symmetry-breaking scale.
  Quite surprisingly, particle physics experiments can provide constraints on
such a new force, even if it is extremely weak, the corresponding gauge
coupling being extremely small (<< 10^-19 !). An ``equivalence theorem'' shows
that a very light spin-1 U boson does not in general decouple even when its
gauge coupling vanishes, but behaves as a quasimassless spin-0 particle, having
pseudoscalar couplings proportional to 1/F. Similarly, in supersymmetric
theories, a very light spin-3/2 gravitino might be detectable as a quasi
massless spin-1/2 goldstino, despite the extreme smallness of Newton's
gravitational constant G_N, provided the supersymmetry-breaking scale is not
too large.
  Searches for such U bosons in \psi and \Upsilon decays restrict F to be
larger than the electroweak scale (the U actually becoming, as an axion, quasi
``invisible'' in particle physics for sufficiently large F). This provides
strong constraints on the corresponding new force and its associated EP
violations. We also discuss briefly new spin-dependent forces.
