present many unknowns as the origin of the asymmetry of the lv-diagram of the Central Molecular Zone (CMZ). On the other hand, there are recent evidences in the stellar component of the presence of a nuclear bar that could be slightly lopsided. Our goal is to characterize the nuclear bar observed in 2MASS maps and to study the gas dynamics in the inner Milky Way taking into account this secondary bar. We have derived a realistic mass distribution by fitting the 2MASS star counts map of Alard (2001) with a model including three components (disk, bulge and nuclear bar) and we have simulated the gas dynamics, in the deduced gravitational potential, using a sticky-particles code. Our simulations of the gas dynamics reproduce successfully the main characteristics of the Milky Way for a bulge orientation of 20 DEG-35 DEG with respect to the Sun-Galactic Center (GC) line and a pattern speed of 30-40 km/s/kpc. In our models the Galactic Molecular Ring (GMR) is not an actual ring but the inner parts of the spiral arms, while the 3-kpc arm and its far side counterpart are lateral arms that contour the bar. Our simulations reproduce, for the first time, the parallelogram shape of the lv-diagram of the CMZ as the gas response to the nuclear bar. This bar should be oriented by an angle of 60 DEG-75 DEG with respect to the Sun-GC line and its mass amounts to (2-5.5) 109 \Msun. We show that the observed asymmetry of the CMZ cannot be due to lopsidedness of the nuclear bar as suggested by the 2MASS maps. We do not find clear evidences of lopsidedness in the stellar potential. We propose that the observed asymmetry of the central gas layer can be due to the infalling of gas into the CMZ in the l=1.3 DEG-complex.