  In quantum field theory, a consistent prescription to define and deform
integration contours in the complex energy plane is needed to evaluate loop
integrals and compute scattering amplitudes. In some nonlocal field theories,
including string field theory, interaction vertices contain transcendental
functions of momenta that can diverge along certain complex directions, thus
making it impossible to use standard techniques, such as Wick rotation, to
perform loop integrals. The aim of this paper is to investigate the viability
of several contour prescriptions in the presence of nonlocal vertices. We
consider three ``different'' prescriptions, and establish their (in)equivalence
in local and nonlocal theories. In particular, we prove that all these
prescriptions turn out to be equivalent in standard local theories, while this
is not the case for nonlocal theories where amplitudes must be defined first in
Euclidean space, and then analytically continued to Minkowski. We work at
one-loop level and focus on the bubble diagram. In addition to proving general
results for a large class of nonlocal theories, we show explicit calculations
in a string inspired nonlocal scalar model.
