The results of work on creating methods, models, computational algorithms for remote preventive health monitoring systems are presented, in particular, cardiac preventive monitoring. The main attention is paid to the models and computational algorithms of preventive monitoring, the interaction of the computing kernels of a remote cluster with portable ECG recorders, implantable devices and sensors. Computational kernels of preventive monitoring are a set of several thousand interacting automata of analog of Turing machines, recognizing the characteristic features and evolution of the hidden predictors of Atrial Fibrillation(AF) ,Ventricular tachycardia or fibrillation (VT-VF), sudden cardiac death, Heart Failure (HF) revealed by them. The estimation of the time for reaching the boundaries heart events is calculated on the basis of the evolution equations for the ECG multi-trajectories determined by recognizing automata. Evaluation time of heart events (HE) boundaries to achieve is calculated on the basis of the evolution equations for ECG multi-paths defined by recognizing machines. Ultimately, the computational cores reconstruct the ECG of the forecast and give temporary estimates of its achievement. Cloud computing cluster supports low-cost ECG ultra-portable recorders and not limits the possibilities of using a more complex patient telemetry containing wearable and implantable devices: CRT and ICD, CardioMEMS HF System etc.