The current list of 264 well-determined original orbits of long-period comets (Marsden 1989) includes 18 hyperbolic orbits with negative binding energies -1/a0 exceeding 4 x 10(-5) AU. According to Yabushita (1991) this is the upper limit compatible with the nongravitational accelerations of outgassing cometary nuclei, and higher values may be indicative of interstellar origin. Analysis of the published orbit computations shows that for 10 of the 18 suspect comets (1895 IV, 1898 VIII, 1904 II, 1911 IV, 1932 VII, 1940 III, 1959 III, 1968 VI, 1975 XI, 1986 XVII) the hyperbolic excess is within the range of computing uncertainty even for a purely gravitational solution. In another five cases (1953 II, 1957 III, 1960 II, 1971 V, 1989 XIX) nongravitational solutions yield positive values of 1/a0, and in two cases (1899 I and 1955 V) the remaining excess is smaller than its mean error. A difficult exception is comet 1976 I, but a detailed analysis of its observations has shown that they can be satisfied by an elliptic original orbit without the inclusion of nongravitational effects (Kresak 1992). Statistical analysis of various properties of the quasi-hyperbolic comets makes it possible to identify the sources of the computed hyperbolic excesses. These are, in particular, splits of cometary nuclei implying the loss of exact identity, and outbursts changing the appearance of the central condensation. Such events are rather irregularly distributed in time, concentrating around 1957, and cannot be described by any simplified model of nongravitational accelerations. Orbital elements T, q and i, affecting the observing conditions in several respects, also play a significant role. All of these effects tend to increase the dispersion of the computed original binding energies. Accordingly, the real proportion of new comets and their degree of clustering around the aphelion distance of about 60 000 AU is greater than generally assumed; and there is no evidence for any comet coming from the interstellar space.