The phosphorescence of phenazine (PZ) and quinoxaline (QX) was investigated after pulsed laser excitation in the glass-transition range of several alkane solvents. Three relaxation processes of PZ and QX in the metastable triplet state, T-1, were studied as a function of temperature: (1) the decay of the selective population of the strongly phosphorescent triplet substate T-1, due to spin-lattice relaxation (SLR), (2) the time-dependent red shift of the phosphorescence spectrum due to the solvation of triplet-state molecules, and (3) the decay of the phosphorescence polarization due to orientational relaxation (OR). Various aspects and connections of the mechanisms governing the three relaxation phenomena are discussed. The relaxation dynamics were characterized at temperatures above the glass-transition temperature of the respective solvent, where the fundamental processes involved are strongly dependent upon the solvent viscosities. For the systems treated here, OR and solvation were satisfactorily described by a Vogel-Fulcher-Tammann temperature behavior. SLR also depends on properties of the alkane solvent above the glass transition. Upon cooling, SLR becomes independent of the specific solvent proper-ties and is based on mechanisms that are typical for amorphous glasses or solids. (This particular aspect will be the subject of a subsequent publication, part 2).