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We describe a family of calibrations arising naturally on a hyperk\"ahlermanifold $M$. These calibrations calibrate the holomorphic Lagrangian,holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is anHKT (hyperkaehler with torsion) manifold with holonomy $SL(n, {\Bbb H})$, weconstruct another family of calibrations $\Phi_i$, which calibrates holomorphicLagrangian and holomorphic coisotropic subvarieties. The calibrations $\Phi_i$are (generally speaking) not parallel with respect to any torsion-freeconnection on $M$.

Calibrations in hyperkahler geometry