Two new basic complex rheological models of ideal materials, fractional type are defined by structural formulas and constitutive relations. A new rheological element the fluid—Newton's ideally viscous fluid flow, fractional type, was introduced. A new rheological modified basic complex Kelvin-Voigt's model, fractional type, was defined in parallel coupling of rheological Newton's ideally viscous fluid flow, fractional type with rheological Hooke's ideally elastic material element. By series linking the new rheological element the fluid—Newton's ideally viscous fluid flow, fractional type with the rheological Hooke's ideally elastic material element, a new modified rheological model complex Maxwell's model of fractional type is defined, which is one of the two rheological basic complex models of ideal materials. Two new rheological dynamic systems of the fractional type, oscillator or crawler type were formed as rheological dynamic systems, which in their structure contain, as a link, standard light rheologic models of the fractional type, defined as complex rheological models of materials, fractional type. Their dynamics are described by differential equations of fractional order and the dualities of their dynamics are shown. The emergence of internal degrees of freedom of movement was indicated. Series of the graphs are presented.