The melting temperatures of Li, Na, K, Rb, and Cs versus pressure were measured to 32 kbar in a piston cylinder apparatus with hydrostatic pressure medium and in situ pressure measurements. The accuracies in pressure and temperature are ± 0.4 % and ± 0.25° C, respectively. Substantial deviation from measurements using solid, non-hydrostatic pressure media is observed. The adiabat, (δT/δP)s,was measured to 32 kbar and 400°C by adiabatic compression. Ln (δT/δP)s is a linear function of volume with good consistency in the slopes. (δT/δP)s changes insignificantly at the liquid-solid phase transitions. The Grüneisen parameters, calculated from γ = Bs/T (δT/δP)s, decreases with pressure and temperature. Bs is the adiabatic bulk modulus. The γ-volume curves show strong curvature and γ tends to become volume independent at compressions of about 30 %. γ increases by several percent at the liquid-solid transition.