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The velocity spectrum of metastable H(2S) atoms produced by electron bombardment of $H2$ has been measured by a time-of-flight technique. Two distinct groups of metastables have been detected. The slower atoms are interpreted as arising from transitions to attractive states just above the H(1S)+H(2S) dissociation limit. The absence of very slow atoms may indicate maxima in the relevant excited state potential curves at large internuclear separation. The faster atoms probably arise from transitions to doubly excited repulsive states, such as $(2s\sigma )(2p\sigma )1.3\Sigma u+$, The fast atom spectrum shows a strong dependence on observation angle.