This work was motivated by the goal of removing the hypothesis of simple connectedness from the rational homotopy theory of D. Sullivan. %as set forth in \bibref[5].%\break To a simply connected space $\bd X$ is associated it's rational localization $\ph:\bd X\to\bd X_0$, %\break and to the differential graded algebra $\bd A(\bd X)$ of rational polynomial forms on $\bd X$ it's Sullivan minimal model $\ps:\bd M\to\bd A(\bd X)$. It is shown that the minimal model $\bd M$ is dual to the Postnikov tower of $\bd X_0$. Thus $\bd M$ determines the rational homotopy type of $\bd X.$\par \quad In the present paper we have eliminated the simply connected hypothesis from the first part of the theory. Working in the category of semi-simplicial complexes, we show that if $\bd X$ is a one pointed Kan complex, and P is a family of prime integers, there exists a semi-P-localization $f:\bd X\to\bd X_p$ such that $f_*:\pi_1(\bd X)\to\pi_1(\bd X_p)$ %\break is an isomorphism and $f_*:\pi_k(\bd X)\to\pi_k(\bd X_p)$ is P-localization of abelian groups, %\break $k\ge 2$. Semi- P-localization is also characterized by a universal mapping property, and the fact that $f$ induces isomorphisms on twisted coefficient cohomology whenever the coefficients are in a $\zp$-module.