The value of the critical current (fc)-critical field (Hc) of cold-worked Nb, Mo-Re and Nb-Zr wires at constant temperature is not a single-valued function of the field and current direction. The previous history of a specimen during an experiment plays an important role and a measurement of the critical field-critical current value can influence the response of the specimen to subsequent measurements. Anomalous resistive transitions are observed when Ic, vs Hc, curves are determined by proceeding from low to high fields which may not occur in measurements proceeding from high to low fields. Further, it is possible to condition a specimen to enable it to reach maximum values of the critical field and critical current. This phenomenon is also encountered in the operation of superconducting solenoids. The polarity of the field and current during this treatment is found to be significant. The effects of the rate increase of the current, of rotating the Specimen in a transverse field, and of current density and temperature have also been studied.