Thirteen peach [Prunus persica (L.) Batsch] fruit characteristics were investigated for 3 years, 1993, 1994, and 1995, in College Station, Texas, to determine heritability, genetic and phenotypic correlations, and predicted response to selection. Seedlings of 108 families resulting from crosses among 42 peach cultivars and selections were used in the evaluations. A mixed linear model, with years treated as fixed and additive genotypes as random factors, was employed to analyze the data. Best linear unbiased prediction (BLUP) was used to estimate fixed effects. Restricted maximum likelihood (REML) was used to estimate variance components, and a multiple trait model was used to estimate genetic and phenotypic covariances between traits. Genetic and phenotypic correlations ≥0.65 and <0.30 were considered strong or very strong and weak, respectively. Date of ripening, fruit development period (FDP) and date of full bloom had the highest heritability (h2) estimates, 0.94, 0.91, and 0.78, respectively. Fruit cheek diameter and titratable acidity (h2 = 0.31) were the traits with the lowest estimates. Fruit development period, fruit blush, and date of ripening had the highest predicted selection responses, whereas fruit suture, fruit cheek, L/W12 (ratio fruit length to average fruit diameters), and fruit tip had the lowest values. Most genetic correlations were ≥0.30 and were, in general, much higher than the corresponding phenotypic correlations. All four measures of fruit size were genetically and phenotypically very strongly correlated. Important genetic correlation estimates were also observed for date of ripening with FDP (ra = 0.93), date of ripening and FDP with fruit blush (ra = -0.77, ra = -0.72), SS (percent soluble solids) (ra = 0.63, ra = 0.62) and TA (ra = 0.55, ra = 0.64), and SS with TA (ra = -0.56). Direct selection practiced solely for early ripening and short FDP is expected to have a greater effect on correlated traits than direct selection for early bloom and large fruit mass.