The present study was carried out with the purpose of generating information related to genetic improvement of pipiana squash, with the following objectives: to estimate, for 14 traits, the genetic parameters: mean, additive variance, dominance variance, heritability, coefficient of additive variation and phenotypic correlations, and to learn the effect of different plant densities in the agronomic performance of squash. The experiments were established in 2001 in Chapingo, Mexico, in two locations and at two plant densities per location: D1: 13,890 and D2: 9,260 plants·ha-1 of squash in association with maize (50,000 plants·ha-1) in alternating rows of each crop species. Results indicated that additive variance was of 15,184 for fruit weight and 35.98 for seed weight. When selection was practiced, dominance variance appeared. Additive variation coefficients were less than 15 % in 13 out of 14 studied characters, and heritabilities oscillated between 20.35 and 88.39 %. Seed weight (SW) varied with location and plant density, and it was higher at density one in San Martin (SW: D1=68 g·plant-1, D2=62.09 g·plant-1) and at density two in San Juan (SW: D1=74.60 g·plant-1, D2=78.40 g·plant-1).