Experimental results of magnetization and neutron diffraction in the temperature range 300-1100K evidence an anomalous high-temperature irreversible magnetic behavior on metastable FeCu solid solutions. When the temperature is increased above 500K , a segregation process takes place in the as-milled sample which gives rise to the appearance of Fe (bcc) and Cu (fcc) phases. Further heating shows that the magnetization at 850K falls down due to the temperature dependence of the bcc-Fe magnetization and the onset of the alpha-gamma martensite transformation. The temperature of this martensite phase transition (1020K) is more 100K lower than that of pure alpha-Fe (1183K) . On cooling from high temperatures (1100K) , the magnetization does not appreciably increase its value until the temperature is lowered below 900K , showing a broad hysteresis between the forward (warming) and the reverse (cooling) transformations. Apart of the above mentioned bcc-Fe and fcc-Cu phases, on cooling, a small amount of isolated gamma-Fe precipitates (≈5%) is detected. Further heating above 600K show a large magnetization enhancement, reaching a value 50% higher with respect to the value measured at room temperature. During cooling from 1100K the maximum value of magnetization is not recovered. The origin of this anomalous high temperature magnetic behavior is explained on the basis of strong magnetovolume instabilities in gamma-Fe . Furthermore, the thermal expansion coefficient of the gamma-Fe precipitates (21-23×10-6K-1) , obtained from the neutron-diffraction patterns, is in excellent agreement with that calculated theoretically ( 20-24×10-6K-1 , along the studied temperature range 300-1100K ). This fact is a signature of an anti-Invar behavior in gamma-Fe precipitates that could explain this surprising magnetic response.