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We present Giant Meterwave Radio Telescope (GMRT) observations of the HI 21 cm line and Very Large Array (VLA) observations of the OH 18 cm line from the Seyfert 2 galaxy Mrk 1. HI emission is detected from both Mrk 1 and its companion NGC 451. The HI emission morphology and the velocity field of Mrk 1 are disturbed. We speculate that the nuclear activities of Mrk 1 are triggered by tidal interactions. We estimate the HI masses of Mrk 1 and NGC 451 to be 8.0(±0.6)x10⁸M_☉ and 1.3(±0.1)x10⁹M_☉ respectively. We have also detected the HI 21 cm line and the OH 18 cm line in absorption toward the nucleus of Mrk 1 at a blueshifted velocity with respect to its systemic velocity indicating an outflow of atomic and molecular gas. Two OH lines, at 1665 and 1667 MHz, are detected. Each of the profiles of the HI and OH absorption consists of two components that are separated by ∼125km/s. Gaussian fitting gave dispersions of ∼44 km.s^–1 for both the components of the HI absorption. The profile of the OH absorption is qualitatively similar to that of the HI absorption. Both components of the OH absorption are thermally excited. The peak optical depths of the two components of the HI absorption are (7.3±0.4)x10^–2 and (3.2±0.4)x10^–2. The corresponding peak optical depths of the 1667 MHz OH absorption are (2.3±0.3)x10^–2 and (1.1±0.3)x10^–2. The higher velocity components of the HI and OH (1667 MHz) absorption lines are blueshifted from the [OIII]λ5007, [OI]λ6300, and the systemic velocity by ∼100 km.s^–1, but are consistent with the [OII]λ3727 velocity. We explain these velocity discrepancies as due to shock ionization of a region which is pushed forward due to shocks in front of the radio nucleus thereby giving apparent blueshift to HI, OH, and [OII] velocities. The optical depth ratios τ_HI/τ_OH¹⁶⁶⁷ of both the components of the HI and OH absorption are ∼3, indicating their origin in dense molecular clouds. Using OH/A_v values for the Galactic molecular clouds, we obtain 9<A_v<90 toward the line of sight of Mrk 1.