We present measurements of the superconducting and charge-density-wave (CDW) critical temperatures (T c and T CDW ) as a function of pressure in the transition metal dichalchogenides 2H -TaSe 2 and 2H -TaS 2 . Resistance and susceptibility measurements show that T c increases from temperatures below 1 K up to 8.5 K at 9.5 GPa in 2H -TaS 2 and 8.2 K at 23 GPa in 2H -TaSe 2 . We observe a kink in the pressure dependence of T CDW at about 4 GPa that we attribute to the lock-in transition from incommensurate CDW to commensurate CDW. Above this pressure, the commensurate T CDW slowly decreases, coexisting with superconductivity within our full pressure range.