Two existing estimators use inferred relationship information on a pair-wise level: regression of the phenotypic similarity of a pair of individuals on an estimate of their relationship and a likelihood procedure that maximises the probability of their genotypic and phenotypic observations. Computer simulation was used to compare the behaviour of these approaches. Bias in estimates of heritability decreased with increasing sample size, decreased heritability, increasing relatedness and increasing sample size. The regression approach showed less bias than the likelihood approach, but much larger sampling variance. A modified form of the likelihood technique, requiring fewer initial assumptions about population parameters was developed, which showed lower bias in its estimates of heritability than the likelihood technique originally proposed. An alternative approach in which marker-information was used to reconstruct sibships through relationship assignment within a single generation using Markov chain Monte Carlo (MCMC) techniques was developed. The reconstructed sibships were assumed correct and analysed using restricted maximum likelihood under an animal model. Simulations to compare the properties of estimates with those made using existing techniques indicated that sibship reconstruction was, in many cases, superior to earlier methods, regaining family-specific weighting lost through pair-wise analysis, having lower mean squared errors and showing only slight downwards bias, provided that there was sufficient marker information. Equations appropriate for MCMC analysis of half-sib, full-sib and hierarchical sib-ship structures are presented. The approaches were extended so that information from other types of marker loci, for example mitochondrial or dominant loci, known maternal information and additional variance parameters can be incorporated into the analysis. Analysis using the technique was made of feral population of Soay sheep, with body weight being used as an example trait. Results indicated that the Soay population has a low level of relatedness and so heritability estimates were not reliable, unless inferred relationship data was used only to augment an existing set of known relationships.