This paper presents results of petrophysical whole core analyses carried out in highly permeable dolomite cores, intensively vugular and fractured. The estimated parameters were: multi-directional permeability tests kHθ and kv, matrix ϕmab and fracture porosity ϕfb, the high velocity flow coefficient β, relative permeabilities to oil and water, the effective oil permeability (as a function of effective stress), capillary functions, and the variation of absolute permeability with temperature. The temperature and effective hydrostatic stress used ranged up to 150°C and 20 000 psi, respectively. Several sleeve materials were tested, finding that silicon withstood successfully the test conditions. Stainless steel was used for the flow screens needed for the horizontal permeability measurements. The fluids used in these tests were nitrogen, helium, and brine. As an example of the values estimated for some of these parameters, the ratios for horizontal to vertical permeabilities at an standard effective stress of 400 psi were kh0°/kv = 117, kh90°/kv = 17, and kh0°/kh90° = 6.87. The ratio of matrix to fracture porosities ϕmab/ϕfb = 9.15 and for the compressibilities cfb/cmab = 5.56. Finally, specific values of matrix porosity and multidirectional permeabilities for an increment of the effective stress conditions from 1000 to 8000 psi, resulted in a decrease of 23% for the total 78% for vertical permeability. A new correlation for the high-velocity coefficient is presented for conditions of these highly macrovugular formations, which approximately is parallel 1.6 log cycles above the Firoozabadi and Katz correlation.