Motivated by a simplified multiperipheral model, we formulate a general qualitative description of the momentum spectrum of secondaries, resulting from a collision of two hadrons at high energies. Arguing from two fundamental multiperipheral concepts, (a) that transverse momenta are limited and (b) that distant particles on the multiperipheral chain are uncorrelated, we predict that at sufficiently high incident energies, the momentum spectrum of particle $X$ in the reaction $a+b\to X$+anything, when presented in the variables $p_{\perp }$ and $y=invsin\left[\frac{p_{\parallel }}{{({p_{\perp }}^2+m_{X^2})}^{\frac{1}{2}}}\right]$, develops a central plateau in the $y$ dependence, which elongates and flattens to a value that is normalized by the total cross section as the incident energy increases. Moreover, it is shown that the resultant particle density distribution is consistent with the hypothesis of limiting fragmentation. We contrast this description with the predictions of the two-fireball model, the isobar-pionization model, and the statistical thermodynamical model.

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