A sample of contact binaries discovered by the OGLE project in Baade's Window, with orbital periods longer than one day and with available color and light-curve data, has been analyzed. It consists of only 32 systems, in contrast to 388 WUMa-type systems with shorter periods which were analyzed before. Most systems are very distant and are probably located close to or in the galactic Bulge. Two groups of contact binaries are seen in the sample: (1) a continuation of the WUMa-type sequence, extending up to the orbital periods of 1.3 - 1.5 day, but rather sharply ending in this period range; (2) an inhomogeneous group of rare systems with long periods up to 26 days, all with red colors and relatively shallow eclipses. While the systems of the first group share most of the characteristics of the typical WUMa-type systems (except that they are on the average brighter and more distant, hence more reddened), the long-period systems do not seem to form an early-type extension of contact binaries, but may consist of a mixture of late-type objects, including tidally distorted red giants with invisible companions.

24 pages including 10 figures (inserted with psfig) and one table; submitted to AJ