Type 1 insulin-like growth factor receptor (IGF1R) is a membrane-spanning glycoprotein of the insulin receptor family that has been implicated in a variety of cancers. The key questions related to molecular mechanisms governing ligand recognition by IGF1R remain unanswered, partly due to the lack of testable structural models of apo or ligand-bound receptor complexes. Using a homology model of the IGF1R ectodomain IGF1RDeltabeta, we present the first experimentally consistent all-atom structural models of IGF1/IGF1RDeltabeta and IGF2/IGF1RDeltabeta complexes. Our explicit-solvent molecular dynamics (MD) simulation of apo-IGF1RDeltabeta shows that it displays asymmetric flexibility mechanisms that result in one of two binding pockets accessible to growth factors IGF1 and IGF2, as demonstrated via an MD-assisted Monte Carlo docking procedure. Our MD-generated ensemble of structures of apo and IGF1-bound IGF1RDeltabeta agrees reasonably well with published small-angle X-ray scattering data. We observe simultaneous contacts of each growth factor with sites 1 and 2 of IGF1R, suggesting cross-linking of receptor subunits. Our models provide direct evidence in favor of suggested electrostatic complementarity between the C-domain (IGF1) and the cysteine-rich domain (IGF1R). Our IGF1/IGF1RDeltabeta model provides structural bases for the observation that a single IGF1 molecule binds to IGF1RDeltabeta at low concentrations in small-angle X-ray scattering studies. We also suggest new possible structural bases for differences in the affinities of insulin, IGF1, and IGF2 for their noncognate receptors.