  A definition of frames for Krein spaces is proposed, which extends the notion
of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\HH,
\K{\,}{\,})$ is in particular a frame for $\HH$ in the Hilbert space sense. But
it is also compatible with the indefinite inner product $\K{\,}{\,}$, meaning
that it determines a pair of maximal uniformly $J$-definite subspaces with
different positivity, an analogue to the maximal dual pair associated to a
$J$-orthonormal basis.
  Also, each $J$-frame induces an indefinite reconstruction formula for the
vectors in $\HH$, which resembles the one given by a $J$-orthonormal basis.
