The anomalous volume contraction &ohgr;a(T) of Fe‐Ni and Fe‐Pt Invar alloys were analyzed in terms of the Gru¨neisen equation using the experimental data of thermal expansion coefficient. It was found that &ohgr;a(T) increases with increasing Fe composition or temperature and remains nonzero even above the Curie point &Vthgr; ffor both the Invar alloys. The susceptibility of Fe‐Ni alloys and the magnetization of Fe‐Pd alloys were measured. The magnetic anomalies of Invar alloys are summarized. A calculation by molecular field theory in terms of a high and low spin state transition model can well explain the anomalous isothermal magnetization curve and the anomalous volume contraction as well as instability of ferromagnetism, where the center of the low spin state has higher energy than the high spin state at high temperatures and the distribution of low spin state energy and the exchange field of the high spin state were considered. From the x‐ray diffraction experiments at low temperatures, an anomalous random static displacement (?2s)1/2was obtained after subtracting the mean‐square displacement of the lattice vibration of Fe‐Ni Invar. Such a displacement may come from the mixed state of high and low spins.