Experimental data for nucleus-nucleus collisions at the CERN SPS suggest that an ideal hadron gas model is unable to account simultaneously (same baryonic chemical potential and temperature at freeze-out) for the strange anti-baryon to baryon ratios and pion abundances. Using a thermodynamically consistent excluded volume model we examine possibilities to account for the observed excess of pions.The formation of systems at high energies and densities allows the study of matter in another regime which, it is hoped, is amenable to the use of equilibrium statistical physics. Of particular interest is the possibility for the formation of a short-lived phase transition to a quark-gluon plasma (QGP). Recently nucleus-nucleus collisions have been performed at the BNL AGS (14 A GeV) and the CERN SPS (200 A GeV) producing energetic systems in which such a phase transition is hoped to take place. However, it is first necessary to understand predictions from conventional hadron physics before one can draw conclusions about any new phenomena which may be observed.Assuming local thermodynamical equilibrium at the final (freeze-out) stage of the process, particle number ratios can be calculated without detailed knowledge of the very complicated and poorly understood dynamics of heavy ion collisions. Strange particle production has attracted special attention as a possible signal of QGP formation [1, 2]. Hadron gas models have been successful in reproducing many of the observed hadron ratios measured at the AGS and SPS [3,4,5,6,7,8]. However for SPS data it has been observed [9, 4, 5, 6] that a simple ideal gas model is unable, within a single set of freeze-out parameters, to simultaneously yield the strange anti-baryon to baryon ratios together with pion to proton and charged particle ratios D Q = (N + − N − )/(N + + N − ) (N + and N − are the positive and negative charged hadron multiplicities). Note that N + − N − ∼ = p, N − ∼ = π − (p, π − are proton and negative pion multiplicities) and hence D Q ∼ = (1 + 2π − /p) −1 . It appears that the chemical freeze-out values of temperature T and baryonic chemical potential µ b found in Refs. [9,4,5,6] from the SPS data for strange particles are in a contradiction with the large pion/nucleon ratio. As D Q can be related to the entropy of the system, hadron gas models appear unable to account for the large entropy per baryon at freeze-out [9]. Therefore, unexpectedly, not strange particles but the deficiency of pions in the hadron gas model calculations is the main problem in the theoretical hadron gas interpretation of the SPS particle production data. Several mechanisms of the two-stage hadron chemical freeze-out [5] and QGP breakup to hadrons [9,5] have been proposed to remedy this problem but without significant success.The large values of T and µ b found in hadron gas models suggest that the chemical freeze-out state in the SPS experiments looks rather like a hot dense hadron gas and one needs a non-ideal gas equation of state to describe the system. In Refs. [7,8] a non-ideal fo...