Abstract : Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from R n to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: "polynomial", "absolute value", "max" and "min" and such a program will be called a semipolynomial expression. It will be proved, using the ordinary Real Positivstellensatz, a general Real Positivstellensatz concerning the semipolynomial expressions. Using this semipolynomial version for the Real Positivstellensatz we shall get as consequences a continuous and rational solution for the 17-th Hilbert problem, rational and continuous versions for several cases in the Real Positivstellensatz and constructive proofs for several theorems concerning the algebra over the real numbers.