  This work investigates whether the observed 1^-+ exotic mesons are molecular
states. We first use a potential model to calculate the spectra and lifetimes
of the f_0(980) and a_0(980), taken to be loosely bound molecular states of K
Kbar, then apply the same scenario to the 1^-+ exotic states pi_1(1400) and
pi_1(1600), assuming them to be pi eta(1295) and pi eta(1440) molecules
respectively. We derive the effective potential in the framework of field
theory at the hadronic level. Our results indicate that the present data on
pi_1(1400) and pi_1(1600) rule out the specific molecular ansatz. We show that
the lifetime of a loosely bound heavy-light molecule with enough angular
momentum is fully determined by the lifetimes of its constituent mesons.
