Alkali fluoroborate glasses are readily formed in the compositional range from zero alkali fluoride to 45 mol% LiF or 55 mol% NaF or KF. The density, refractive index, thermal expansion coefficient, glass transformation temperature, transformation range viscosity and electrical conductivity have been measured. Trends in the properties of these glasses as a function of composition exhibit behaviour similar to that observed for alkali borate glasses including the borate anomaly in thermal expansion coefficient and glass transformation temperature. A new borate anomaly has been found for the refractive index of these glasses. A structural model based on the replacement of BO4 tetrahedra by BO3F tetrahedra is proposed which explains the differences in behaviour between these glasses and the corresponding alkali borate glasses.