  A scalar valued random field is called operator-scaling if it satisfies a
self-similarity property for some matrix E with positive real parts of the
eigenvalues. We present a moving average and a harmonizable representation of
stable operator scaling random fields by utilizing so called E-homogeneous
functions. These fields also have stationary increments and are stochastically
continuous. In the Gaussian case critical H\"{o}lder-exponents and the
Hausdorff-dimension of the sample paths are also obtained.
