Marching algorithms are the rule rather than the exception in the determination of pressure distribution in long multiphase-flow pipes, both for the case of pipelines and wellbores. This type of computation protocol is the basis for most two-phase-flow software and it is presented by textbooks as the standard technique used in steady state two-phase analysis. Marching algorithms acknowledge the fact that the rate of change of common fluid flow parameters (such as pressure, temperature, and phase velocities) are not constant but vary along the pipe axis while performing the integration of the governing equations by dividing the entire length into small pipe segments. In this algorithm, governing equations are solved for small single sections of pipe at a time, and the calculated outlet conditions for the particular segment and then propagated to the next segment as its prescribed inlet condition. Calculation continues in a "marching" fashion until the entire length of the pipe has been integrated. In this work, several examples are shown where this procedure cannot longer accurately represent the physics of the flow. The implications related to the use of this common technique are studied, highlighting its lack of compliance with the actual physics of the flow for selected examples. This paper concludes by suggesting remedies to these problems, supported by results, showing considerable improvement in fulfilling the actual constrains imposed by the set of simultaneous fluid dynamic continuum equations governing the flow.