  We develop a new nonrelativistic effective field theory of $\rho$NRQCD [1] to
describe the finite lifetime effects in the threshold production of top
quark-antiquark pairs. The theory is based on the expansion in a parameter
$\rho=1-m_W/m_t$ characterizing the dynamics of the top-quark decay. Within
this framework we compute the nonresonant contribution to the total cross
section of the top quark-antiquark threshold production in electron-positron
annihilation up to the next-to-next-to-leading order. Our method naturally
resolves the problem of spurious divergences in the analysis of the unstable
top production.
