The four general double-adiabatic invariants governing ideal MHD flow in a narrow flux tube are summarized and are put in a form suitable for calculation of flow in tubes of nonconstant cross- sectional area. Results for converging-diverging (Laval-type) flux tubes are developed and compared to single-adiabatic results which are identical to those for ordinary gasdynamic flow. As in such flows, a transition from subsonic to supersonic double-adiabatic flow requires the presence of a minimum in the flux tube area, i.e., a maximum in the field strength. With increasing subsonic values of the parallel Mach number, M∥=v(&rgr;/3p∥)1/2, as the plasma moves toward the field maximum where M∥=1, the density, &rgr;, in double-adiabatic flow initially increases rather than decreases, behavior that is the exact opposite of that in ordinary gasdynamics. A density maximum occurs at the subsonic value M∥=(1-p⊥/3p∥)1/2; for larger M∥ values, the density then decreases monotonically as in ordinary gasdynamics. The two pressures, p∥ and p⊥, behave in qualitatively the same was as &rgr;. A fifth invariant, valid for general two-dimensional (∂/∂z≡0; Vz≠0; Bz≠0) single- or double-adiabatic field-aligned flow, is derived. Such two-dimensional flows over slender obstacles are then analyzed by use of linear theory. It is found that in certain parameter regimes the governing equation for the vector potential is elliptic and can be reduced to Laplace's equation by simple stretching of one coordinate. In other regimes the equation is hyperbolic, indicating the presence of standing wave patterns. The relevance of these results to flow over magnetopause undulations, including flux transfer events, is discussed briefly; actual quantitative applications will be presented in a subsequent paper. (D. W. Walthour et al., submitted, 1992). ¿ American Geophysical Union 1992