Records form Finnish Ayrshire cattle were used to estimate variances and covariances of milk traits by the restricted maximum likelihood (REML) method using the individual animal model (IAM). Two data sets were analyzed. The first data set consisted of 1423 sires and 16363 cows, of which 11911 had records on first lactation. The heritabilities estimated from this data set for milk yield, protein yield, protein content and fat content were 0.40, 0.31, 0.63 and 0.68, respectively. The second data set was a subset of first data set with herds with less than ten observations excluded and consisted of 1335 sires and 11262 cows with 8140 first, 5688 second and 3717 third lactation records. The heritability estimates from the second data set under a repeatability model for milk yield, protein yield, protein content and fat content were 0.30, 0.26, 0.59 and 0.66, respectively. The repeatability estimates for the same traits were 0.53, 0.51, 0.67 and 0.76, respectively. The second data set was also used to estimate genetic and phenotypic correlations among milk traits in first lactation. Both genetic and phenotypic correlations among protein yield and protein and fat content traits were small. The genetic correlation between milk yield and protein content was -0.61, between milk yield and fat content -0.50 and between protein content and fat content 0.67. Absolute values of phenotypic correlations for the same pairs of traits were somewhat smaller than respective genetic correlations.