  We study a combinatorial object, which we call a GRRS (generalized reflection
root system); the classical root systems and GRSs introduced by V. Serganova
are examples of finite GRRSs. A GRRS is finite if it contains a finite number
of vectors and is called affine if it is infinite and has a finite minimal
quotient. We prove that an irreducible GRRS containing an isotropic root is
either finite or affine; we describe all finite and affine GRRSs and classify
them in most of the cases.
