The fruit of the ei<ght genera of the Ptychosperma alliance have complex sclerenchymatous endocarps that typically consist of a palisade layer derived from the locular epidermis, some sclerified ground tissue, and vascular bundles with thick fibrous sheaths. Hi<ghly integrated endocarps appear to have evolved in at least six different lines in the alliance, and unspecialized forms can be found in several genera. The exocarp consists of fibrous bundles and brachysclereids, and also shows varying degrees of integration. Although it is difficult to separate the large genera from one another upon pericarp characters alone, small genera, subgenera, and groups of species often separate readily, sutggesting that the major taxonomic application of data from the pericarp will be at the infrageneric level in this alliance. In this paper, the first in a series presenting histological investigations into the structure of the pericarp in the palm family (Palmae or Arecaceae), the informal groups of Moore's (1973) classification will be followed, beginning with the Ptychosperma alliance of the arecoid group. The present research grew out of a taxonomic study of Ptychosperma (Essig, 1975) in which certain histological features of the pericarp were found to be of taxonomic significance. Earlier studies (Guerin, 1949; Murray, 1971, 1973) indicated that pericarp histology might provide important systematic information in many groups of palms. Guerin (1949) made a broad, descriptive survey of palm fruits with representatives from most of the major groups in the family. Though he provided much useful information, he did not analyze his data in a taxonomic framework and did not discuss the phylogenetic or ontogenetic implications of the data. Murray (1971) covered in depth the ontogeny and structure of a relatively few examples from six of the major groups of palms-the coryphoid, chamaedoreoid, pseudophoenicoid, caryotoid, arecoid, and cocosoid groups. Later she published a special analysis of the formation of the endocarp (Murray, 1973), a work providing valuable information on the origin and ontogeny of the various tissues in palm fruits, adding another dimension to Guerin's data. In the work of both authors it is evident that there is great structural diversity in palm fruits that might be exploited in taxonomic and evolutionary studies, as has long been recognized by taxonomists such as Moore (1957). The purpose of the present series of investigations is to augment the base of data established by Guerin, Murray, and others, to synthesize 1 I thank Harold E. Moore, Jr., and Natalie W. Uhl for making the preserved fruit collection of the L. H. Bailey Hortorium available to me and for providing valuable comments on the manuscript, and my wife, Yau-Ping, for technical assistance. 2 Biology, University of South Florida, Tampa FL 33620.