  We discuss the path integral representation for the fermionic particles and
strings and concentrate at the problems arising when some target-space
dimensions are compact. An example of partition function for fermionic particle
at finite temperature or with one compact target-space dimension is considered
in detail. It is demonstrated that the first-quantized path integral requires,
in general, presence of nonvanishing "Wilson loops" and modulo some common
problems for real fermions in Grassmannian formulation one can try to
reinterpret them in terms of condensates of the world-line fermions. The
properties of corresponding path integrals in string theory are also discussed.
