Dissolution of synthetic methane and carbon dioxide hydrates was monitored after their transport to the ocean floor at 1000m depth. Cylindrical test specimens were initially grown in the laboratory by combining either cold, pressurized methane gas or pressurized liquid CO2 with sieved granular water ice, then heating the reactants through the H2SO melting point. Samples were then hydrostatically compacted to near-zero porosity, with resulting geometry of approximately 2.5 cm in diameter by 3-4 cm in length. Two samples each of methane and carbon dioxide hydrate were placed in a custom-made sample display rack having individual compartments for each sample with a transparent polycarbonate front window, and side and back walls of a flexible fine-mesh screen that permitted seawater flow around the hydrates. The sample rack was then transferred to the ocean in a stainless steel transport vessel pressurized with 10 MPa methane using the (ROV). On the seafloor, the sample display rack was removed from the pressure vessel and secured in a stand attached to an autonomous underwater video recorder system using a time programmable Hi8 video recorder. The samples were continuously monitored for 2.30 h using HDTV camera system, then followed by 20.75 h observation with the autonomous Hi8 time-lapse camera system (15 s every 0.25 h), and additional 3.33 h HDTV observation at the end of the experiment. Loss of volume and dissolution rates of the hydrates were derived from the measurement of the change of the projected diameter of the individual samples over time. During the first 2.30 h, the diameter of the two CO2 hydrates decreased from 22 mm to 15 and 13 mm, respectively. Diameter loss followed a generally linear trend of 0.94 and 1.20 $\m/sec, corresponding to a dissolution rate of 13 to 17 mole O${2}$/m$^{2}$h. Similar short-term oscillations about this linear trend were observed on both samples, suggesting a link to bottom current velocity. The CH${4}$ hydrates dissolved much more slowly, with a diameter loss rate of 0.09 to 0.097 $\m/sec, corresponding to 1.2 to 1.4 mole CH${4}$/m$^{2}$h. The ratio of the dissolution rates of the CO${2}$ and CH${4}$ hydrates can be readily explained using a diffusive sub layer model for gas hydrate dissolution. Given the similarity of the diffusion coefficients of methane and CO${2}$, the ratio of their dissolution rates should be given by the ratio of their solubility's under the ambient P,T-conditions. We calculated the solubility's of methane and CO${2}$ in the presence of hydrates using the Redlich-Kwong-Soave equation-of-state and the gas hydrate model of van der Waals and Plateeuw and derive a ratio of the solubility's of 10.5, which is in close agreement with our hypothesis. The fast dissolution rate of CO${2}$-hydrate is comparable to the rate of dissolution of liquid CO${2}$, which implies that gas hydrate formation has no major consequences for the residence time of CO${2}$ in a "deep-sea lake" CO$_{2}$- sequestration scenario. The dissolution of several mm methane hydrate per day in undersaturated seawater implies that long-term survival of seafloor hydrate outcrops observed today must be sustained by hydrate regrowth. Changes in the appearances of such outcrops on sites visited over time could be explained simply by dissolution, without the assumption of changes in bottom temperatures or detachment of buoyant solid hydrate structures.