Pseudodifferential operators of several variables are formal Laurent series
in the formal inverses of $\partial_1, ..., \partial_n$ with $\partial_i = d$
$1 \leq i \leq n$. As in the single variable case, Lax equations can be
constructed using such pseudodifferential operators, whose solutions can be
provided by Baker functions. We extend the usual notion of tau functions to the
case of pseudodifferential operators of several variables so that each Baker
function can be expressed in terms of the corresponding tau function.