Genetic interference means that the occurrence of one crossover affects the occurrence and/or location of other crossovers in its neighborhood. Of the three components of genetic interference, two are well modeled: the distribution of the number and the locations of chiasmata. For the third component, chromatid interference, there exists only one model. Its application to real data has not yet been published. A further, new model for chromatid interference is presented here. In contrast to the existing model, it is assumed that chromatid interference acts only in the neighborhood of a chiasma. The appropriateness of this model is demonstrated by its application to three sets of recombination data. Both models for chromatid interference increased fit significantly compared to assuming no chromatid interference, at least for parts of the chromosomes. Interference does not necessarily act homogeneously. After extending both models to allow for heterogeneity of chromatid interference, a further improvement in fit was achieved. DURING meiotic prophase 1 in diploid individuals, each chromosome is paired with its homologue. Each homologue is duplicated, producing two identical chromatids, the sister strands. A crossover represents an event where two nonsister chromatids form chiasmata, break, and reunite, enforced by the tight contact and the twisting between the chromatids and the subsequent repair mechanism. After meiosis, one of the four resulting gametes is randomly chosen for further inheritance. For clarity we use the term chiasma at the four-strand stage, while the term crossover is used with single strands or gametes. Hence, from one nonsister strand chiasma, two crossovers result. An example of a meiosis at the four-strand stage is given in Figure 1. It has often been proven that chiasma or crossover events are not independent. The notion of genetic interference describes the effect on crossovers of neighboring crossovers. The components of interference are as follows: Non(complete)randomness in the number of crossovers: The no-interference model applies if the crossover numbers are Poisson distributed. All other count distributions yield deviations from no interference. Non(complete)randomness in crossover locations: The suppression of nearby crossovers has been modeled by nonuniformly distributed locations and by nonexponentially distributed intercrossover distances with renewal point processes. Chromatid interference (CI): The strands actually involved in a crossover depend in some way on those strands involved in neighboring crossovers. Substantial progress has been made in investigating and modeling the first two components. For these cases we use the term suppression interference (SI). For SI models, no chromatid interference (NCI) is assumed. For recent reviews see Karlin and Liberman (1994) and McPeek and Speed (1995). The χ2-model of recombination (Fosset al. 1993; Zhaoet al. 1995a) is accepted as a satisfying model for positive SI. Negative SI, i.e., one chiasma enforcing the occurrence of another one, can be described, for example, by a negative binomial count distribution for the number of chiasmata. The investigation of CI has not reached the same level yet. It started in the 1930s when recombination fractions >0.5 had been observed. This phenomenon was termed pseudolinkage. Models have been developed for data exhibiting pseudolinkage (Winge 1935; Mather 1938). Particularly, Mather found that this phenomenon could result only from CI. However, little evidence was found for it in diploid organisms. For a review and a test procedure, see Zhao et al. (1995b). Recently, Zhao and Speed (1998, 1999) developed a model for CI. To our knowledge, an application has not been published so far. Summarizing the literature, the general view is that CI is not evident. This is reflected by widely distributed mapping software (e.g., CRIMAP) that reduce recombination fractions >0.5 to 0.5. Yet, recombination fractions θ > 0.5 are accepted in tetraploids. Recombination fractions of up to 0.8 have been found in tetraploid fish (Wrightet al. 1983). Since θ ≤ 0.5 is valid even for tetraploid species under NCI [see formula (6) with Q = 0.25], there is evidence for an action of CI. Hence, CI cannot be excluded, either from a theoretical point of view, or from empirical evidence. It therefore appears to be helpful to derive alternative models to the existing model of Zhao and Speed (1998), either to increase the evidence for CI in diploids or to strengthen the conviction that there is none. The objective of the present study was to develop a model allowing parallel nonsister strand chiasmata, which could not arise under high SI if one assumes suppression on all four strands, and sister strand chiasmata, which also have not been modeled so far but could play a role at high SI. In analyzing a number of recombination data sets we found evidence for SI and CI. Until now heterogeneity of interference has not been investigated. We incorporated CI heterogeneity into both CI models and obtained further improvement in fit.