The viscoelastic properties of hot melt pressure-sensitive adhesives (HMPSA) based on formulations of block copolymers and tackifying resins have been studied in detail, through the variation of the complex shear modulus, G*, as a function of frequency, ω. In this first article, we analyze the individual behavior of the components of HMPSA blends: (1) the two copolymers, styrene-isoprene (SI) diblock copolymer and styrene-isoprene-styrene (SIS) triblock copolymer and (2) two tackifying resins. The viscoelastic behavior of the overall formulation is also presented. We have mainly studied the effects of (1) the molecular characteristics of the SI and SIS copolymers and (2) the composition of the blends (mainly the effect of SI content, S content in SIS and SI, resin content) on the viscoelastic properties. A theoretical approach based on concepts of molecular dynamics leads to a model which describes reasonably well the linear viscoelastic properties of individual components and their formulations. Our systematic study can be used to design new copolymer molecules which can mimic the rheological behavior and end-user properties of regular formulations at room temperature.