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