Porous materials allow for easier osseointegration of implants and their firmer connection with the bone. The presence of pores in a material may become a source of both mechanical and corrosion problems. The presented study explored a Ti-39Nb alloy with a porosity of 0-33%. Specimens were exposed in the physiological solution of two pH values. In view of this material's possible use in dental applications, the effect of fluoride ions on its corrosion behaviour was studied. The open circuit potential and polarization resistance were measured. Data concerning susceptibility to crevice corrosion were obtained from potentiostatic measurements based on the ASTM F746 standard. In terms of corrosion behaviour, specimens with a lower porosity were not much different from the non-porous material. Porosity produced its effect at the level of 24 and 33%. It is obvious that porosity affects corrosion behaviour of this type of material. This conclusion was confirmed by measurements of susceptibility to crevice corrosion which grew with the specimens' increasing porosity. Corrosion resistance of the Ti-39Nb alloy was comparable with that of the compact material, but the presence of pores initiated a local attack of the material.