The 1977-78 annual Graduate Student Survey analyzes information supplied by graduate physics students and also includes graduate astronomy students. Highlights of the findings are: a continuing decline in the number of graduate physics degree recipients; the reassurance of a steadily improving job market for new physicists with graduate degrees; a five percentage-point decrease in the proportion of graduates who accepted postdoctorates with a corresponding increase in employment offers with potential permanence; and a decline in astronomy enrollments and graduate degree recipients. Data are presented on the following areas: employment offers for new physics doctorate and masters recipients, 1973-78; characteristics of the graduate physics student population, 1977-78; characteristics of minority-group graduate physics students; graduate physics students by subfield and years of graduate study completed, 1977-78; sources of support by sex and degree status; number of advanced graduate physics students specializing in selected experimental or theoretical subfields by years of graduate study completed; type of research performed by doctoral candidates with respect to years of graduate study completed; employment offers for 1977-78 doctorate recipients by subfield and type of research; type of employer and work activity of physics terminal masters; and characteristics of astronomy graduate students and doctorate recipients. (SW)