Stochastic differential equations driven by Gaussian processes with dependent increments and related market models with memory In the last ten years fractional Brownian motion BHt received a lot of attention (e.g. [Be] [GrNo] [HuOk] [HuOkSa] [So] [DeUs] [Oh] and [DuHuPa]). This process has dependent increments which make it interesting for many applications such as finance (e.g. [HuOk] [Be]) and network simulations (e.g. [No]). However BHt has a covariance function E(BHt BHs ) which depends only on the Hurst parameter H 2 (0 1). It follows for example that one cannot model a process with short range dependency with BHt . As a generalization a class of centered Gaussian processes with dependent increments Bvt is defined. If Bvt is used as noise process it is often important to have an integral driven by this process.Several authors defined the stochastic integral driven by fractional Brownian motion RR XsdBHs . In order to use this integral to explain stochastic differential equations it is desirably that the stochastic integral driven by fractional Brownian motion has expectation value 0. If the integral is defined by use of the Wick product ([Be] [HuOk]) the expectation value of the stochastic integral driven by BHt is zero.