First-principles full-potential linear muffin-tin orbital calculations have been used to study RuO2 in the fluorite (CaF2) and rutile structures. An investigation of the effects of metal and nonmetal alloying, oxygen vacancies, and lattice strain on the phase stabilities and electronic structure has been made. From these theoretical results suggestions on how the cubic phase may be stabilized are made. The pressure induced phase transitions between the rutile, CaCl2, Pa3 and fluorite phases and the bulk moduli of several 4d and 5d transition metal dioxides have also been studied.