  A concept of boundedness of L-index in joint variables (see in Bordulyak M.T.
The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud.,
4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc
function. We proved criteria of boundedness of $\mathbf{L}$-index in joint
variables which describe local behaviour of partial derivative and give an
estimate of maximum modulus on a skeleton of polydisc. Some improvements of
known sufficient conditions of boundednees of $\mathbf{L}$-index in joint
variables are obtained.
