We present a Herschel/SPIRE survey of three protoclusters at z=2-3 (2QZCluster, HS1700, SSA22). Based on the SPIRE colours (S350/S250 and S500/S350) of 250 $��$m sources, we selected high redshift dusty star-forming galaxies potentially associated with the protoclusters. In the 2QZCluster field, we found a 4-sigma overdensity of six SPIRE sources around 4.5' (~2.2 Mpc) from a density peak of H$��$ emitters at z=2.2. In the HS1700 field, we found a 5-sigma overdensity of eight SPIRE sources around 2.1' (~1.0 Mpc) from a density peak of LBGs at z=2.3. We did not find any significant overdensities in SSA22 field, but we found three 500 $��$m sources are concentrated 3' (~1.4 Mpc) east to the LAEs overdensity. If all the SPIRE sources in these three overdensities are associated with protoclusters, the inferred star-formation rate densities are 10$^3$-10$^4$ times higher than the average value at the same redshifts. This suggests that dusty star-formation activity could be very strongly enhanced in z~2-3 protoclusters. Further observations are needed to confirm the redshifts of the SPIRE sources and to investigate what processes enhance the dusty star-formation activity in z~2-3 protoclusters.

15 pages, 5 figures, 12 tables, Accepted for publication in MNRAS