We developed a space-time model to project seasonal streamflow extremes on a river network for at several lead times. In this, the extremes – 3-day maximum streamflow - at each gauge location on the network are assumed to be realized from a Generalized Extreme Value (GEV) distribution with temporal non-stationary parameters. The parameters are modeled as a linear function of suitable covariates. In addition, the spatial dependence of the extremes across the network is modeled via a Gaussian copula. The parameters of the non-stationary GEV at each location are estimated via maximum likelihood, whereas those of the Copula are estimated via maximum pseudo-likelihood. Best subset of covariates are selected using AIC. Ensembles of streamflow in time, which are based on the varying temporal covariates and from the Copula, are generated, consequently, capturing the spatial and temporal variability and the attendant uncertainty. We applied this framework to project spring (May-Jun) season 3-day maximum flow at seven gauges in the Upper Colorado River Basin (UCRB) network, at 0 ~ 3 months lead time. In this basin, almost all of the annual flow and extremes that cause severe flooding, arrives during the spring season as a result of melting of snow accumulated during the preceding winter season. As potential covariates, we used indices of large scale climate teleconnection – ENSO, AMO, and PDO, regional mean snow water equivalent and temperature from the preceding winter season. The skill of the probabilistic projections of flow extremes is assessed by rank histograms and skill scores such as CRPSS and ES for marginal and spatial performance. We also evaluate the utility of Gaussian Copula by computing spatial threshold exceedance probabilities compared to a model without the Copula – i.e. independent model at each gauge. The validation indicates that the model is able to capture the space-time variability of flow extremes very well, and the skills increase with decreasing lead time. Also the use of climate variables enhances skill relative to using just the snow information. The median projections and their uncertainties are highly consistent with the observations with a Gaussian copula than without it, indicating the role of spatial dependence. This framework will be of use in long leading planning of flood risk mitigation strategies.