In this paper, we consider the perturbed Stark operator Hu = H 0 u + qu = −u ′′ − xu + qu, where q is the power-decaying perturbation. The criteria for q such that H = H 0 + q has at most one eigenvalue (finitely many, infinitely many eigenvalues) are obtained. All the results are quantitative and are generalized to the perturbed Stark type operator.By induction, we can define V (ξ) and φ(ξ, E j ) for all j = 1, 2, · · · , N on (0, J w + N T w+1 ] = (0, J w+1 ]. Now we should show that the definition satisfies the w + 1 step conditions (64)-(68). Let us pick up R(ξ, E j ) for some E j ∈ B. R(ξ, E j ) decreases from point J w + (j − 1)T w+1 to J w +jT w+1 , and may increase from any point J w +(m−1)T w+1 to J w +mT w+1 , m = 1, 2, · · · , N and m = j. That isand for m = j,by Theorem 6.1. Thus for j = 1, 2, · · · , N ,This leads to (66). By the same arguments, we have for j = 1, 2, · · · , N and ξ ∈ [J w , J w+1 ],This implies (67) for w + 1. By the construction of V (ξ), we have for ξ ∈ [J w +tT w+1 , J w +(t+1)T w+1 ] and 0 ≤ t ≤ N −1,