  The longitudinal polarisation transfer from muons to lambda and anti-lambda
hyperons, D_LL, has been studied in deep inelastic scattering off an
unpolarised isoscalar target at the COMPASS experiment at CERN. The spin
transfers to lambda and anti-lambda produced in the current fragmentation
region exhibit different behaviours as a function of x and xF . The measured x
and xF dependences of D^lambda_LL are compatible with zero, while
D^anti-lambda_LL tends to increase with xF, reaching values of 0.4 - 0.5. The
resulting average values are D^lambda_LL = -0.012 +- 0.047 +- 0.024 and
D^anti-lambda_LL = 0.249 +- 0.056 +- 0.049. These results are discussed in the
frame of recent model calculations.
