  We propose a new construction of an integrable hierarchy associated to any
infinite series of Frobenius manifolds satisfying a certain stabilization
condition. We study these hierarchies for Frobenius manifolds associated to
$A_N$, $D_N$ and $B_N$ singularities. In the case of $A_N$ Frobenius manifolds
our hierarchy turns out to coincide with the KP hierarchy; for $B_N$ Frobenius
manifolds it coincides with the BKP hierarchy; and for $D_N$ hierarchy it is a
certain reduction of the 2-component BKP hierarchy. As a side product to these
results we illustrate the enumerative meaning of certain coefficients of $A_N$,
$D_N$ and $B_N$ Frobenius potentials.
