  (abridged) We present the first results of our deep survey of lensing
clusters aimed at constraining the abundance of star-forming galaxies at
z~6-10. Deep near-IR photometry of two lensing clusters (A1835 and AC114) was
obtained with ISAAC/VLT. These images, combined with existing data in the
optical bands, including HST images, were used to select very high redshift
candidates at z>~6 among the optical-dropouts. We have identified 18(8) first
and second-category optical dropouts in A1835 (AC114), detected in more than
one filter up to H(Vega)~23.8 (AB~25.2,uncorrected for lensing). Among them,
8(5) exhibit homogeneous SEDs compatible with star-forming galaxies at z>~6,
and 5(1) are more likely intermediate-redshift EROs based on luminosity
considerations. We have also identified a number of fainter sources in these
fields fulfilling our photometric selection and located around the critical
lines. We use all these data to make a first attempt at constraining the
density of star-forming galaxies present at 6<z<10 using lensing clusters.
Taken at face value, it appears that the number of candidates found seems to be
higher than the one achieved in blank fields with similar photometric depth in
the near-IR. The luminosity function derived for z>6 candidates appears
compatible with that of LBGs at z~3. The turnover observed by Bouwens et al.
(2005) towards the bright end relative to the z~3 LF is not observed in this
sample. Also the upper limit for the UV SFR density at z~6-10 is compatible
with the usual values derived at z~5-6, but higher than the estimates obtained
in the NICMOS Ultra Deep Field (UDF). Increasing the number of blank and
lensing fields with ultra-deep near-IR photometry is essential to get more
accurate constraints on the abundance of z>6 galaxies.
