Fluorophosphate glasses of the Ba(PO3)(2)-MgF2-CaF2-AlF3 system exhibit anomalous behavior, in regard to the glass-transition temperature (T-g) and the coefficient of thermal expansion (alpha(CTE)), at a fluoride concentration of similar to 36 mol%. A similar trend in the infrared band absorption coefficient (alpha(IR)) at 2170 cm(-1) of the overtone of 2 nu(ss)(OPO) and/or a combination of nu(as)(OPO)+nu(as)(POP) fundamental vibrations of PO4 tetrahedra also has been observed, relative to changes in the glass composition. Statistical analyses have shown that the T-g and alpha(CTE) values are correlated with alpha(IR) at 2170 cm(-1) by linear equations. The thermal properties of some of the glasses have been calculated using these equations, to test their validity and utility. The experimental property values of the glasses present a very good fit of data within a 95% confidence interval of the calculated mean values.