We have fabricated unstressed gallium-doped germanium (Ge:Ga) far-infrared photoconductors for astronomical observations in space. A photoconductor's size as small as 0.5 by 0.5 by 0.5 mm3 is designed to reduce the influence of cosmic high-energy particles. The concentration of Ga in the Ge crystal is 1 X 1014 cm-3. The responsivity of this type of Ge:Ga photoconductor has been improved by decreasing the Ga concentration from 2 X 1014 cm-3 to 1 X 1014 cm-3. Extrinsic semiconductor photoconductors, such as Ge:Ga, which operate at low temperature (less than 4.2 K) and low background photon influx (less than 1 X 108 photons/sec) for space infrared astronomy, have undesirable behavior such as spike noise, hook response, and slow transient response. These phenomena limit the usefulness of the device as a photodetector. The optimum operating temperature of our Ge:Ga photoconductors at which we get the best noise equivalent power (NEP) is 3 K. The response to step increase in influx has a large amplitude with a time constant within 1 sec. This transient response of the photoconductor can be fitted by the model with three time constants. The curve-fitting shows the existence of a component with a time constant of around 0.05 - 0.5 sec, which we define as a moderate-fast transient response. We derived the time constant and the amplitude fraction of the moderate-fast transient response as a function of bias fields at several temperatures. The amplitude ratio of this component to the total response decreases as the bias field increases, and the time constant shortens as the operating temperature rises. Following, we estimated hole life time at the low temperature and under the low background photon influx from hole mobility and responsivity. Moreover, we found good agreement between the time constant of the moderate-fast transient response to the transient time that Hiromoto et al. (1992) pointed from a two-region model of a Ge:Ga photoconductor with ion- planted ohmic contact.