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An alternative approach to the classical Morel-Voevodsky stable motivichomotopy theory $SH(k)$ is suggested. The triangulated category of framedbispectra $SH_{nis}^{fr}(k)$ and effective framed bispectra$SH_{nis}^{fr,eff}(k)$ are introduced in the paper. Both triangulatedcategories only use Nisnevich local equivalences and have nothing to do withany kind of motivic equivalences. It is shown that $SH_{nis}^{fr}(k)$ and$SH_{nis}^{fr,eff}(k)$ recover the classical Morel-Voevodsky triangulatedcategories of bispectra $SH(k)$ and effective bispectra $SH^{eff}(k)$respectively.  We also recover $SH(k)$ and $SH^{eff}(k)$ as the triangulated category offramed motivic spectral functors $SH_{S^1}^{fr}[\mathcal Fr_0(k)]$ and thetriangulated category of framed motives $\mathcal {SH}^{fr}(k)$ respectivelyconstructed in the paper.

The triangulated categories of framed bispectra and framed motives