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We report observations of 47 candidate protostars in two optically thick lines (H2CO 212 − 111 and CS 2 − 1) and one optically thin line (N2H + 1 − 0) using the IRAM 30-m, SEST 15-m, and Haystack 37-m radio telescopes. The sources were selected from the redness of their spectra (Tbol < 200 K) and their near distance (d < 400 pc). Most of the sources have asymmetric optically thick lines. The observed distribution of velocity differences, δV = (Vthick − Vthin)/∆Vthin, is skewed toward negative (blue-shifted) velocities for both the H2CO and CS samples. This excess is much more significant for Class 0 than for Class I sources, suggesting that we detect infall motions toward Class 0 and not toward Class I sources. This indicates a difference in the physical conditions in the circumstellar envelopes around Class I and Class 0 sources, but does not rule out the presence of infall onto Class I sources by e.g. lower opacity gas. Bipolar outflows alone, or rotation alone, cannot reproduce these statistics if the sample of sources has randomly oriented symmetry axes. We identify 15 spectroscopic infall candidates, of which 6 are new. Most of these infall candidates have primarily turbulent rather than thermal motions, and are associated with clusters rather than being isolated. Subject headings: Stars:formation, ISM:kinematics and dynamics, ISM:molecules 1.