We show hot the processes e(-)e(+) --> ZH,gamma H, which will be studi
ed at LEP2 and at high energy colliders, could be used to search for t
ypes of New Physics (NP) characterized by an effective NP scale in the
few TeV range and affecting the scalar sector only. In particular, fo
r e(-)e(+) --> ZH, we propose the measurement of suitable azimuthal as
ymmetries determined from the angular distribution of the Z-decay plan
e with respect to the Z-production one. Such asymmetries, together wit
h the ZH angular distribution, may allow a complete disentangling of t
he five dimension-6 operators O-UB, O-UW, (O) over bar(UB), (O) over b
ar(UW), O-Phi 2, describing the residual NP effects to the Higgs coupl
ings. We note that the first four of these operators contribute to pro
cesses relevant to LEP1 precision measurements only at the 1-loop leve
l, while the last operator remains completely unconstrained at this le
vel. The process e(-)e(+) --> gamma H is also very sensitive to NP and
should bring important independent information.