  Following J.D. Murray, we consider a system of two differential equations
that models traveling fronts in the Noyes-Field theory of the
Belousov-Zhabotinsky (BZ) chemical reaction. We are also interested in the
situation when the system incorporates a delay $h\geq 0$. As we show, the BZ
system has a dual character: it is monostable when its key parameter $r \in
(0,1]$ and it is bistable when $r >1$. For $h=0, r\not=1$, and for each
admissible wave speed, we prove the uniqueness of monotone wavefronts. Next, a
concept of regular super-solutions is introduced as a main tool for generating
new comparison solutions for the BZ system. This allows to improve all
previously known upper estimations for the minimal speed of propagation in the
BZ system, independently whether it is monostable, bistable, delayed or not.
Special attention is given to the critical case $r=1$ which to some extent
resembles to the Zeldovich equation.
