It follows from a theorem of Markov that the minimum number of negation gates in a circuit sufficient to compute any Boolean function on n variables is l = ⌊log n⌋ + 1. It can be shown that, for functions computed by families of poly­nomial size, O(log n) depth and bounded fan-in circuits (NC¹), the same result holds: on such circuits l negations are necessary and sufficient. In this paper we prove that this situation changes when polynomial size circuit families of constant depth are considered: l negations are no longer sufficient. For threshold circuits we prove that there are Boolean functions computable in constant depth (TC⁰) such that no such threshold circuit containing o(n^ε), for all ε > 0, negations can compute them. We have a matching upper bound: for any ε > 0, everything computed by constant depth threshold circuits can be so computed using n^ε negations asymptotically. We also have tight bounds for constant depth, unbounded fan-in circuits (AC⁰): n/log^r n, for any r, negations are sufficient, and Ω(n/log^r n), for some r, are necessary.